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Tag Archives: architecture
Cisco deepens enterprise network virtualization, security detection of DNA suite – Network World
Posted: February 22, 2017 at 3:49 am
Cisco today announced a variety of hardware, software and services designed to increase network virtualization and bolster security for campus, branch office and cloud customers.
The products, which include a Network Functions Virtualization branch office device and improved security network segmentation software, fall under Ciscos overarching Digital Network Architecture plan. DNA offers integrated networking softwarevirtualization, automation, analytics, cloud service management and security under a single suite.
+More Cisco News on Network World: Cisco reserves $125 million to pay for faulty clock component in switches, routers+
DNA offers IT leaders a blueprint for building digital ready networks. In just under 18 months we have seen over1,900 organizations deploy our SDN controller, APICEM, in their networks and start laying a foundation capable of enabling their digital transformation, said Ciscos Prashanth Shenoy, vice president of marketing, Enterprise Networking and Mobility.
On the hardware side, Cisco rolled out the Enterprise Network Compute System (ENCS) 5400 Series, a 1RU Intel Xeon server that includes an eightport GE Switch which supports LTE, T1, DSL and more, as well as DualPhy Gigabit Ethernet WAN connectivity and 64Gb of memory.
The 5400 a purposebuilt branch platform aimed at helping customers accelerate their Enterprise NFV deployments by extending routing, security, WAN optimization and other network services to their branch environments, Shenoy said.
The 5400 is all about the speed and agility in setting up a branch office rollout that secures virtualized services,” Shenoy said. A branch office that took days to set up and provision previously can now be done virtually in minutes with security, QoS and management capabilities.
Cisco does offer other SDWAN packages and the 5400 is another option but one that focuses on customers interested in virtualizing network functions, experts said.
For security, Cisco extended its TrustSec security software across all its network components and offers security segmentation to isolate attacks and restrict threats in the network.
TrustSec 6.1 now extends from the campus to the branch office and the cloud, all in an effort to avoid and prevent pervasive threats Shenoy said.
In that vein, Cisco also enhanced its Identity Services Engine (ISE). ISE 2.2 offers much deeper visibility into applications on endpoints, including detection of anomalous behavior. It also offers more granular control with the ability to define “DEFCON” policy sets that lets customers escalate their response to prolific threats, Shenoy stated.
Together ISE and TrustSec can help turn the network into a sensor and enforcer, Cisco said. ISE provides visibility and control of users and devices on the network, while TrustSec provides softwaredefined segmentation to isolate attacks and restrict movement of threats in the network.
Rather than changing the authorization of individual users and devices, or implementing policy changes manually, changing DEFCON state changes the TrustSec policies defining how users, devices, and systems can talk to others essentially raising the network drawbridges to protect your critical data and maintaining essential services. For example, you could define DEFCON 4 to kick all guests off the network, DEFCON 3 to kick all BYOD users off the network, DEFCON 2 to restrict peertopeer traffic, and DEFCON 1 to severely limit access to your crown jewels, wrote Kevin Skahill, director, product management in Ciscos Secure Access and Mobility Product Group in a blog detailing the new security software.
ISE 2.2 also provides streamlined workflows that include guest, secure access, and BYOD setup with Cisco Wireless LAN Controllers in as little as 10 minutes. This approach also extends to customers migrating from the Cisco Access Control System (ACS), which Cisco recently announced will go endofsale, Skahill stated.
On the services side, Cisco announced an online DNA Advisor and network assessment tool that helps customers define their digital network. The company also announced DNA Advisory Services that will offer indepth consulting to help enterprises formulate a digital strategy.
Cisco dovetailed the DNA announcement with the release of a study that looked at the issues surrounding what it calls digitalready networks. Conducted by IDC and commissioned by Cisco, the research surveyed 2,054 global organizations across 10 countries to determine the digital readiness of their networks. A couple findings from the study included:
Outdated infrastructure characteristics such as manual configuration and management processes, overlay security geared mainly toward external threats, and siloed network domains hinder the networks ability to further the goals of digital business. For IT staff, valuable time is spent keeping the lights on instead of aligning network capabilities with strategic initiatives that improve operational efficiency and enhance customer experience. A network that is truly digital ready is a network that can dynamically align with the everchanging needs of the enterprise. That means a network that allows more agility and faster time to innovation, better security, and greater operational efficiency and simplicity, IDC wrote.
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Cisco deepens enterprise network virtualization, security detection of DNA suite – Network World
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MEPs pass robotics report with key changes – POLITICO.eu
Posted: February 17, 2017 at 1:24 am
An employee of the French Laboratory for Analysis and Architecture of Systems examines a hand of the Pyrene humanoid robot  Remy Gabalda/AFP via Getty Images
Parliament rejected demands for a basic income for workers who lose their jobs and a tax on robots.
By Joanna Plucinska
2/16/17, 1:57 PM CET
Updated 2/16/17, 4:43 PM CET
The European Parliament Thursday passed a controversial report on robotics, but deleted the demands for a basic income for workers who lose their jobs and a tax on robots.
The MEPs, however, supported a European agency for robotics and artificial intelligence, as well as a supplementary fund for victims in accidents in selfdriving vehicles.
Mady Delvaux, the Socialists & Democrats member in the Legal Affairs Committee, drafted the document and was disappointed with the outcome.
Although I am pleased that the plenary adopted my report on robotics, I am also disappointed that the rightwing coalition of ALDE, EPP and ECR refused to take account of possible negative consequences on the job market, she said in a statement.
The report passed 396to123, with 85 abstentions.
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Canadian architecture firm discusses design in the Midwest – Iowa State Daily
Posted: at 1:07 am
Sasa Radulovic and Johanna Hurme from 5468796 Architecture discuss previous projects they have worked on during their lecture Feb. 15. They highlighted the struggle of being creative while operating within the margins. Alex Kelly/Iowa State Daily
The status quo is never easy to change.
Johanna Hurme and Sasa Radulovic discussed Wednesday about how to go about changing the status quo in regard to architecture at Iowa State.
The two are the founders of an architecture firm, 5468796 Architecture, which began in 2007 Winnipeg, Canada. Their discussion focused on a single theme: they believe students and future architects can shape design.
Hurme began the talk by comparing the similarities of Winnipeg to cities in the Midwest.
One of their main points was to show how in many of their designs, they have tried to cut down on interior space in order to expand exterior space.
Its about the stuff that happens between buildings, Hurme said.
The firm believes by doing this, it can offset a trend in much of the United States in the design of apartment and condo buildings, where the living space is cramped, leaving little room for social gatherings.
There is this Finnish word, ‘piha,’ which sort of means collective outdoor space, and as kids we would say we were from the piha, not the building, and we wanted to impose that onto people, Hurme, who is from Helsinki, Finland, said.
A theme that Hurme and Radulovic also discussed was the idea of hyperrationalism in architecture.
We often get accused of doing things for the sake of their aesthetic, but often that way is the best way to do it and [it] becomes necessary, Hurme said.
Radulovic presented a project they worked on that exemplified this thought. Their firm designed an elevated, circular condo building, with two stories of living space. Hurme mentioned that while building an elevated condo may seem irrational, it ended up being the most efficient way for the building to come to existence.
The architects also spent time discussing the business side of their firm and architecture in general.
Its our [architects’] responsibility to know our value, so that we know when we should work for free, or when we should be paid, and how much, Hurme said.
Hurme advised students to avoid putting themselves into the two common boxes the corporate architect and the struggling designer architect and to be successful in whatever way they are able to.
This facet of the discussion is what stood out to senior architecture student Amanda Hoefling.
A lot of the architects that come talk about their projects, but fail to talk about the business side, so I absolutely love how they mentioned that, because thats real life, Hoefling said.
One of the most important topics Hurme and Radulovic talked about was the ability for anyone to make an impact, even in smaller areas such as Winnipeg, or even Ames and Des Moines.
Radulovic said they believe many of their designs have had impacts in their community on social, environmental and economic levels. They have been able to be who they want to be and have success.
One thing that comes from the reality of living in a city with a smaller population is that the feedback you receive from users and people familiar with your project is very quick and direct, Radulovic said.
Throughout the lecture, the pair of architects stressed the importance of staying true to oneself and the ability each design student in the room had to impact the world. It was their belief as well, that the opportunity for impact was greatest by practicing architecture in second and third cities.
Dont abandon the place, make something out of it, Hurme said.
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Canadian architecture firm discusses design in the Midwest – Iowa State Daily
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Cornell Ranks 9th in Producing Unicorn Founders – Cornell University The Cornell Daily Sun
Posted: February 14, 2017 at 10:50 am
data courtesy of Verve
Cornell University ranked in the top ten worldwide for producing the most number of founders of unicorns a term for a billiondollar startup according to a recent study conducted by Verve, a creative search engine optimization company.
The five unicorns founded by Cornell alumni are Lyft, Wayfair, Illumio, Eventbrite, and Human Longevity, which rank 29th, 85th, 150th, 183rd, and 238th respectively in valuation, according to the study.
John Zimmer 06, the cofounder of Lyft, a billiondollar taxi service company based in San Francisco, told Cornell Alumni Magazine that he found inspiration for his company from a city planning class that he took as an undergraduate student in the College of Architecture, Art and Planning.
During a particular lecture on the evolution of U.S. transportation, Zimmer recalled thinking If those are the first three slides in the presentation, what would be the fourth slide ten years from now? Eleven years after Zimmer took the course, Lyft is a now $5.5 billion private company, according to Barnes.
The second unicorn founded by Cornell alumni is Wayfair, a $2 billion online home store founded by Niraj Shah 95 and Steve Conine 95, Barnes added. Shah and Conine called themselves Cornell entrepreneurs at the second Cornell Entrepreneurship Summit in 2013 and also said they found inspiration from their undergraduate courses.
We were three doors apart on our freshmen dorm floor at Cornell and then without really planning it, we ended up starting a company right out of Cornell, Shah said at the summit. The reason we did that [is] we were Cornell engineers. One of the elective courses we took our very last semester was the entrepreneurship course in the Johnson School.
As an assignment for the course, they created a consulting business which quickly paved their career into commercial internet and eventually to their founding Wayfair.
The three remaining unicorns founded by Cornell alumni are valued around $1 billion, according to the research by Verve. Illumio, founded by PJ Kirner 15, is valued at $1 billion; Eventbrite, founded by Renaud Visage 94, M. Eng., is valued at $1.06 billion; and Human Longevity, founded by Robert Hariri 87, M.D. and Ph.D., is valued at $1.2 billion.
The billiondollar startup was once the stuff of myth, which is why private companies worth in excess of $1 billion have come to be dubbed unicorns, said James Barnes, Creative Writer and Researcher for Verve.
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Editor’s Picks #463 – Archinect
Posted: February 11, 2017 at 7:41 am
For the latest in the newish series, Small Studio Snapshots, Nicholas Korody chatted with Los Angelesbased studio MILLINS. Daniel Elmorefelt “these guys sound legit in their intentions and I’m looking forward to seeing what they produce in the future…The rest of the article is uncommonly decipherable for architects”.
Plus, Stefano Colombo,Luca MarulloandEugenio Cosentino went “Looking for a picture that represents something related to the internet and ending up thinking about the desert.”Max Headroom, F.AIA got excited “the phrase ‘last existing encrypted space is genius on many many levels. exciting work!”
News In an interview with NPRs MarketPlace Carl Bass, CEO of Autodesk, explained how computers are superior (in some things) to human designers.JamesJoist got serious
“Spoken like true transhumanist scum; I often think AutoCAD was one of the worst things to happen to architecture. As you might expect the overall reception was poor.”
Reacting to the allfemale lineup for the Carnegie Mellon University School of Architecture’s Spring ’17 lecture series, b3tadine[sutures] quipped “Now I understand why SCIArc couldn’t get any women to lecture, there aren’t any left. Is SCIArc being run by former Jay Leno bookers?”
Steven Holl Architects released plansfor a, pair of white concrete buildings, new Cultural and Health Center in Shanghai.
With I am sure tongue firmly in cheek, archanonymous offered up Mr. Holl some advice “i love your work but if you don’t do an emergency shelter and social housing in the next 5 years you’re never going to get that Pritzker.”tduds chimed in “Really, though, this is beautiful. Holl was a tough sell for me when I was younger but he’s really won me over lately.”
The AIA’s Equity in Architecture Commission Releases Report, with its eleven priority recommendations for action, is required reading.
Mayfair House in London, UK by Squire and Partnersand Charles Street Car Park in Sheffield, UK by Allies and Morrison, are just two of the great projects from the latest Ten Top Images on Archinect’s “Fancy Facades” Pinterest Board.
Firms/Work Updates Farzam Kharvaristarted Radio Architecture a new blog, and introduced himself.
Meanwhile, over at his blog Elemental Urbanism, James Pereirawrote about MaMuCre. Which led Max Headroom, F.AIAto note “David Ruy once said in my grad class Algorithms are recipes. The cooking analogy is great, always thought that was the best analogy and real portrayal of detailing in architecture.”
For anyone looking for a new job and wanting to live in New Orleans,Eskew+Dumez+Rippleis looking to hire a Sustainability Enabler. Or the City and County of San Francisco needs an Urban Designer/Architect.
Anton Romashovbegan sharing photos of architecture (both modern and ancient) in Peru.
School/Blogs
Due to an unexpected surge in applications, the Free School of Architecture (FSA) will significantly increase its inaugural class size for 2017.
For a theory course at UIC, Jamie Evelyn Goldsboroughand her fellow students are researching an architectural typology that has been disrupted / effected by American capitalism. She selected Motels / Hotels. The project is heavily rooted in Eisenman’s Frankfurt Rebstock Competition project of “the Fold.” Jamie also posted a process drawing.
For those interested in a job in academia, University of Kentucky is accepting applications for either an Associate or Full Professor in Interior Design. Or an Associate or Full Professor, Director of Design Technology, with a focus on “developing, implementing and conducting courses that integrate technology within the curriculum.”
UCLAAUD6 put out the call for POOL Issue No.2., submissions of communicative media surrounding the authorities that prescribe, the bodies that obey, and the administrators who implement rules. The deadline is February 20, 2017.
Discussions/Threads
johnshoe was looking for thoughts on the use of anADA Cheat Sheet. The earliest commenters recommended just learning ANSI A117.1 “Learn the code as it’s written. You’ll be more valuable to your firm, the profession, and the general public.”senjohnblutarsky reminded folks of the Adobe “search function”. As tintt sees it “Construction documents are supposed to be clear and concise and not have redundancies or conflicting information.”
mbcube2 is in need of some career advice.Josh Mingsinitial response “I never would have taken such a pay cut. Volunteer is on point.”gruen thought the story sounded familiar “Oh, is NBBJ still up to their old tricks? LOL, legendary.”Contrary to manyshellarchitect counseled sticking it out “Having the local manager on your side is a great ally…I have a hard time believing that people would be purposely deceitful (wishful thinking?)…More likely the decision makers have changed.”
Finally, daerquestioned how to structurally support his staircase, for a school project. Andrew.Circle expanded upon earlier suggestions from archanonymous and Non Sequitur. He also called attention to a deficient for the US guardrail, in the rendering. mightyaa answered the original question simply “Basic Physics” Later randomised posted an example from japan of a gorgeous staircase. (yet tduds nightmare) without a railing.
Additionally
ICYMI, back in November of last year, Keefer Dunn dove “into the failed thinking about the ways in which architecture creates change in order to unpack some of the lessons valuable to architects who are becoming activists and wondering what to do now.”
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Editor’s Picks #463 – Archinect
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Through the looking glass: Tower view showcases progress on Amazon’s unique biospheres – GeekWire
Posted: February 10, 2017 at 3:04 am
The Amazon biodomes as seen from the Doppler tower. (Rod Learmonth Photo)
The everchanging view of the Amazon biospheres is worth marveling at from street level for those who happen to pass through Seattles Denny Triangle area north of downtown.
But viewing the glass orbs from on high creates a unique perspective for anyone who lives orworks around and above thetech giants evolving corporate campus.
The latest view, which showed up in our Facebook feed this week, was shot from Amazons Doppler tower and shows off the three spheres with what appears to be completed glass work. Lit from the inside, one of the domes glows a soft yellow, showcasing what should be a dramatic architectural spectacle when the project is complete.
Set to open in 2018, the 100foottall orbs will house hundreds of species of unique plants, offering employees a oneofakind venue for connecting with nature.
At the GeekWire Summit last October, Scott Wyatt, a partner with the architecture firm NBBJ, which designed the spheres, said they are not a merely a set piece or showpiece.
Its not a showcase for people to come in from the outside, Wyatt said during a talk on modern urban planning. This is for the people that work at Amazon.Its an alternative workplace, a place where you can go be among plants in a profound way.
Showpiece or not, its hard for those of us outside the sphere of Amazon to stop looking.
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Other Voices: Trying to manage the Amazon effect? Don’t ignore … – Modern Materials Handling
Posted: February 9, 2017 at 6:20 am
By MMH Staff February 8, 2017
Editors Note: The following column by J.P. Wiggins, vice president of logistics, 3Gtms, is part of Moderns Other Voices column. The series features ideas, opinions and insights from endusers, analysts, systems integrators and OEMs. Click here to learn about submitting a column for consideration.
Lots of supply chains are dealing with the Amazon effect, which has led consumers to demand lightningfast (and free) delivery times, lastminute order changes, and 100 percent order accuracy. While initially seen as just a retail problem, these expectations have been extended to the B2B world as well.
Managing the Amazon effect requires a host of solutions, but a transportation management system (TMS) is often overlooked. A TMS is critical for the execution of an order, and this is especially true as order cycles shorten and shipment sizes shrink. Any transportation manager would agree that if these customer behaviors arent properly managed, theyre going to drive up costs.
If youre concerned about the demands and expectations around your orders and deliveries, part of the answer may literally be at your fingertips. But please note that not all TMS systems will be able to handle the scenarios and options I describe below. Only a Tier 1, multimodal TMS that was designed in the last several years will have the architecture and flexibility to respond in such a dynamic environment.
Realtime planning A TMS can bridge the gap between the order management system (OMS) and warehouse management system (WMS). By optimizing within the constraints of customer service, it can help consolidate customer orders and find the best mode and carriers to keep costs as low as possible while giving route planners the opportunity to dynamically optimize right up until the freight leaves the warehouse. This includes choosing the best cost/service option for all transportation modes, from parcel to LTL, along with multistop TL, pool distribution, FTL and intermodal while using real rates and services times for all modes.Allowing planners to hold onto freight as long as possible, but still keep releasing freight for shipping as needed, is especially important if trying to consolidate sameconsignee freight as well as building multistop TLs.
A TMS can also shift from being a planning engine to an execution and visibility tool that monitors freight in transit: it knows which orders are on which shipments, along with service times for all modes. It can use logic and workflow to proactively monitor freight and automatically get status and location information from carriers as well as alert and respond automatically. In fact, I know of some shippers that ping their TMS to get the best mode selection and ship date requirements preWMS.
Leveraging pool distribution More and more shippers are seeing order sizes shrink, which makes routing all the more critical. In advanced scenarios, a TMS allows planners to optimize multistop TL freight and build pool distribution (this where a tight integration with both the OMS and WMS is important).
Pool distribution is a longstanding mode of transit that is seeing growth again. Like zone skipping for LTL freight, pool distribution provides a faster and cheaper method of delivery with more visibility and control. Its faster than straight LTL, as you use TL to get the freight to the local terminal and avoid LTL carrier terminal transfers.
With the right TMS, you can handle multileg moves and the associated cost/invoice allocation, which allows you to choose the best pool point and determine which shipments should be picked up or delivered. Routes are kept simple so you can break apart very complex orders and route them each separately. This is what gives you the allimportant tactical savings; it lets you get creative about how you distribute freight and show your customers their savings. Optimizing your distribution network Thanks to ecommerce, many companies are finding that they need to be more than just a fulfilment company. That could mean light assembly, restocking or some other type of specialty tracking service thats required for better customer fulfillment as you create your own differentiators. For niche distributors that operate regionally, a TMS is invaluable. It can find the best partner distributors to act as the delivery agents, along with helping to acquire the freight and pay distributors.
When it comes to the Amazon effect of faster shipment demands, smaller orders, or other customer expectations, dont ignore your TMS. A modern TMS with the right design can operate dynamically and in realtime to help you maximize routes, deliveries, and your customers experience.
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Other Voices: Trying to manage the Amazon effect? Don’t ignore … – Modern Materials Handling
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The Week in Art: Sarah Crowner at the Guggenheim’s Wright Restaurant and Jake and Dinos Chapman in LA – artnet News
Posted: February 6, 2017 at 3:06 pm
Though it may seem that Armory Week and Frieze Week get all the action, the reality is that there is never a dull moment in the New York art world. From the East Side to the West Side, theres always something happening at the citys museums, galleries, and various event spaces. That was the case this week, with the Jake and Dinos Chapmanshow at UTA Artist Space in Los Angeles,timed to the opening of theArt Los Angeles Contemporary fair; the wider Americanart scene also provides plenty of action. Heres a rundown of this weeks highlights.
Celebration for Sarah Crowners NewSiteSpecific Installation at the Solomon R. Guggenheim Museums Wright Restaurant The Guggenheim celebrated the unveiling of new work by Sarah Crowner in its Wright Restaurant with a reception on February 2. Its the first change in decor since the upscale eatery, which previously featured sitespecific work by Liam Gillick, opened in 2009.
Crowners design marries her hardedge geometric painting, on a canvas that hugs the curve of the restaurants back wall, with large, handglazed terracotta tiles in a chevron mosaic pattern, which cover the floor (offwhite), the entry wall (bright yellow), and the wall behind the bar (vibrant sea green). The painting is inspired by a tapestrydesigned by Swedish painter Lennart Reodhe for a Stockholm restaurant in 1961 and made by a Swedish womens weaving collective, and the tiles are the handiwork of her friend and regular collaboratorJos No Suro at hisCermica Suroworkshop in Guadalajara, Mexico.
We brought a little bit of Mexico to the Upper East Side, and thats a beautiful thing! Crowner told guests.
Sarah is very rare in that shes a painter that works with space in a very thoughtful and direct way, Guggenheim curator of contemporary art Katherine Brinson told artnet News. The museum acquired a piece, titled Totem, by Crowner for its permanent collection in 2015, so when it came to redesigning the Wright, I just thought she was a natural choice.
Brinson praised Crowners work on the project, saying she thought in so much depth about how the space would function on a very practical level, but also about this unique building that is, as we say, the greatest artifact in our collection.
Jos No Suro, Sarah Crowner, Guggenheim curator of contemporary art Katherine Brinson, and Guggenheim deputy director Ari Wiseman in front of Crowners Backdrop (after Rodhe, 1961) at the Wright Restaurant at the Guggenheim Museum. Courtesy of Sarah Cascone.
Sarah Crowners sitespecific installation at the Wright Restaurant at the Guggenheim Museum. Courtesy of David Heald/Solomon R. Guggenheim Foundation.
Screening of Jean Nouvel: Reflections at Hearst Tower On February 1, guests gathered to watch Matt Tyrnauers documentary shortJean Nouvel: Reflections, about the Pritzker Prizewinning architect and his ongoing project, at Hearst Towers Joseph Urban Theatre. The evening was hosted by 53W53, the Jean Nouveldesigned condominium that will host the Museum of Modern Arts planned expansion, and the New York Landmarks Preservation. Following a cocktail reception and the screening,Tyrnauer spoke withPaul Goldberger about the making of the film and the career of its subject.
Brandon Haw, Paul Goldberger, Matt Tyrnauer, and Corey Reeser at a screening of Jean Nouvel: Reflections. Courtesy of Star Black.
Caitlin Douglas, George Lancaster, Ken Hsu, and Donna Puzio at a screening of Jean Nouvel: Reflections. Courtesy of Star Black.
Michael Chait, Bertram Beissel Von Gymnich, Jerry Karr, Jasmine Mir, Amanda Ortland, Christina Davis, and Richard Davis at a screening of Jean Nouvel: Reflections. Courtesy of Star Black.
Opening reception for Jake and Dinos Chapmans To Live and Think Like Pigs at UTA Artist Space, Los Angeles January 28 marked the opening reception for UK favorites Jake and Dinos Chapmans new show, titled To Live and Think Like Pigs, at the UTA Artist Space in Los Angeles. In their usual antiaesthetic manner, the brothers aim to startle viewers with compositions that raise questions about religious beliefs, moral standards and political tradition, a topic that feels extremely timely. The show explores darker themes including human decay, Nazi war crimes, Satanism, and conflict. Yet the crowd that turned out for the opening was decidedly not somber, despite the material on view. Spotted in the mix were UTAs Joshua Roth; musician and former husband of Kate Moss, rocker Jamie Hince; musician Courtney Love; and comedians Whitney Cummings and Sebastian Maniscalco.
Lana Gomez, Sebastian Maniscalco, Joshua Roth and Sonya Roth at UTA Artist Space. Photo Stefanie Keenan/Getty Images for United Talent Agency.
Courtney Love and Jamie Hince attend UTA Artist Space. Photo Stefanie Keenan/Getty Images for United Talent Agency.
Dino Chapman and Jake Chapman. Photo Stefanie Keenan/Getty Images for United Talent Agency.
Installation view of To Live and Think Like Pigs, Jake and Dinos Chapmans new show at UTA Artist Space in Los Angeles. Photo Jeff McLane, courtesy the artists.
Art Los Angeles Contemporary Opening at the Barker Hangar The international art world was out in full force in on January 26 for the opening of the Art Contemporary Los Angeles art fair, withPerforma founder RoseLee Goldberg; Ali Subotnick of the Hammer Museum, Los Angeles; Elsa Longhauer of the Institute of Contemporary Art, Los Angeles; curator Douglas Fogle; Sonya Roth of Christies; gallerists Sean Regen,Timothy Blum,and Jeffrey Poe; collectors Anita Zabludowicz and Michael and Susan Hort;Kenny Goss of the Goss Michael Foundation, Dallas; and actresses Eliza Dushkuand Rhea Perlman all in attendance.
In a statement, art advisor Veronica Fernandes called the fair a linchpin to our now exploding contemporary artscenewhere global gallerists, collectors, artists, curators, critics and art advisors crowd each January to engage, build and buy.
Tracy Jeanne Rosenthal of the Los Angeles Reader with Puppies Puppies, Red Carpet. Courtesy the artist and Queer Thoughts, New York. Photo Gina Clyne Photography.
Tim Fleming and guest at Art Los Angeles Contemporary. Courtesy of Art Los Angeles Contemporary, Gina Clyne Photography.
Art Los Angeles Contemporary. Courtesy of Art Los Angeles Contemporary, Gina Clyne Photography.
Huang Rui, Ping Pong 2017. Courtesy of Art Los Angeles Contemporary, Gina Clyne Photography.
Collective Design Studio Tour With Ceramic Artist Peter Lane In advance ofCollective Design, which returns May 37, 2017, the fair hosted a studio visit withPeter Lane in Bushwick, Brooklyn, on January 31. The ceramic artist, who will show his largescale wall installations in an immersive environment at the upcoming fair, offered a behindthescenes tour of the cavernous space, showcasing his artistic process.
Guests included design world influencers such as Yolande Milan Batteau of Callidus Guild,David Mann of MR Architecture + Decor,Francine Monaco and Carl DAquino of DAquino Monaco, andBrook Klausing of Brook Landscape.
In addition to cocktails and conversation, highlights ofthe evening includeda peek at themassive industrialkilns in which Lane fires his work.
Peter Lane shows guests his Bushwick studio. Courtesy of Collective Design.
Peter Lanes Bushwick studio. Courtesy of Collective Design.
Peter Lanes Bushwick studio. Courtesy of Collective Design.
Additional reporting by Eileen Kinsella.
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Trump may fund the Spacex Mars Colonization plan – Next Big Future
Posted: at 2:49 pm
Elon Musk, the founder of SpaceX and Tesla, has made trips to Trump Tower. He met with Trump and the Washington Post has ben reliably told, discussed Mars and publicprivate partnerships.
Elon Musk and SpaceX have the bold dream of colonizing Mars, and think they can launch the first human mission to the surface of the Red Planet as soon as 2024 when Trump, if reelected, would still be in the White House. (We understand that Musk also talked with Trump about other issues, including the need for a smart grid the kind of infrastructure that would give a boost to the solar energy business, in which Musk is a leader via his investments in the company Solar City.)
Trump seems to be cozying up to Elon Musk and is entertaining the idea of financing Musks Mars colonization project
Elon’s Vision of the Mars Colony
Initially, glass panes with carbon fiber frames to build geodesic domes on the surface, plus a lot of miner/tunneling droids. With the latter, you can build out a huge amount of pressurized space for industrial operations and leave the glass domes for green living space.
Real Mars and Spacex Plans
The current Mars plan is:
The Flight Tank for the Interstellar Transport was the most important part of the announcement
The flight tank will actually be slightly longer than the development tank shown, but the same diameter.
That was built with latest and greatest carbon fiber prepreg. In theory, it should hold cryogenic propellant without leaking and without a sealing linker. Early tests are promising.
Will take it up to 2/3 of burst pressure on an ocean barge in the coming weeks.
The spaceship would be limited to around 5 g’s nominal, but able to take peak loads 2 to 3 times higher without breaking up.
Booster would be nominal of 20 and maybe 30 to 40 without breaking up.
Spacex and Elon Musk have the 61 page presentation of the Interplanetary Transport System and the plan from early exploration to a sustainable colony on Mars
Spacex has built a full sized carbon composite fuel tank.
The Interplanetary Transport system can launch 550 tons to low earth orbit which is nearly four times as much as the Saturn V. It would be over four times as powerful as the SLS in the final version of the SLS
Next version of Falcon 9 will have uprated thrust
Final Falcon 9 has a lot of minor refinements that collectively are important, but uprated thrust and improved legs are the most significant.
Elon thinks the F9 boosters could be used almost indefinitely, so long as there is scheduled maintenance and careful inspections. Falcon 9 Block 5 — the final version in the series — is the one that has the most performance and is designed for easy reuse, so it just makes sense to focus on that long term and retire the earlier versions. Block 5 starts production in about 3 months and initial flight is in 6 to 8 months, so there isn’t much point in ground testing Block 3 or 4 much beyond a few reflights.
Robert Zubrin, Longtime Mars Colonization advocate, gives a Critique of the SpaceX Interplanetary Transport System.
Zubrin was struck by many good and powerful ideas in the Musk plan. However, Musks plan assembled some of those good ideas in an extremely suboptimal way, making the proposed system impractical. Still, with some corrections, a system using the core concepts Musk laid out could be made attractive not just as an imaginative concept for the colonization of Mars, but as a means of meeting the nearerathand challenge of enabling human expeditions to the planet.
Zubrin explains the conceptual flaws of the new SpaceX plan, showing how they can be corrected to benefit, first, the nearterm goal of initiating human exploration of the Red Planet, and then, with a costeffective basebuilding and settlement program, the more distant goal of future Mars colonization.
Robert Zubrin, a New Atlantis contributing editor, is president of Pioneer Energy of Lakewood, Colorado, and president of the Mars Society.
Highlights * Have the second stage go only out to the distance of the moon and return to enable 5 payloads to be sent instead of one * Leave the 100 person capsule on Mars and only have a small cabin return to earth * use the refueling in orbit and other optimizations to enable a Falcon Heavy to deliver 40 tons to Mars instead of 12 for exploration missions in 2018, 2020 etc… * Reusable first stage makes rocketplanes going anywhere point to point on Earth feasible. Falcon Heavy would have the capacity of a Boeing 737 and could travel in about one hour of time anywhere
There are videos of the Elon Musk presentation and an interview with Zubrin about the Musk plan at the bottom of the article
Design of the SpaceX Interplanetary Transport System
As described by Musk, the SpaceX ITS would consist of a very large twostage fullyreusable launch system, powered by methane/oxygen chemical bipropellant. The suborbital first stage would have four times the takeoff thrust of a Saturn V (the huge rocket that sent the Apollo missions to the Moon). The second stage, which reaches orbit, would have the thrust of a single Saturn V. Together, the two stages could deliver a maximum payload of 550 tons to low Earth orbit (LEO), about four times the capacity of the Saturn V. (Note: All of the tons referenced in this article are metric tons.)
At the top of the rocket, the spaceship itself where some hundred passengers reside is inseparable from the second stage. (Contrast this with, for example, NASAs lunar missions, where each part of the system was discarded in turn until just the Command Module carried the Apollo astronauts back to Earth.) Since the secondstageplusspaceship will have used its fuel in getting to orbit, it would need to refuel in orbit, filling up with about 1,950 tons of propellant (which means that each launch carrying passengers would require four additional launches to deliver the necessary propellant). Once filled up, the spaceship can head to Mars.
The duration of the journey would of course depend on where Earth and Mars are in their orbits; the shortest oneway trip would be around 80 days, according to Musks presentation, and the longest would be around 150 days. (Musk stated that he thinks the architecture could be improved to reduce the trip to 60 or even 30 days.)
After landing on Mars and discharging its passengers, the ship would be refueled with methane/oxygen bipropellant made on the surface of Mars from Martian water and carbon dioxide, and then flown back to Earth orbit.
Zubrin’s Problems with the Proposed Spacex System
The SpaceX plan as Musk described it contains nine notable features. If we examine each of these in turn, some of the strengths and weaknesses in the overall system will begin to present themselves.
1. Extremely large size. The proposed SpaceX launch system is four times bigger than a Saturn V rocket. This is a serious problem, because even with the companys impressively low development costs, SpaceX has no prospect of being able to afford the very large investment at least $10 billion required to develop a launch vehicle of this scale.
2. Use of methane/oxygen bipropellant for takeoff from Earth, transMars injection, and direct return to Earth from the Martian surface. These ideas go together, and are very strong. Methane/oxygen is, after hydrogen/oxygen, the highestperforming practical propellant combination, and it is much more compact and storable than hydrogen/oxygen. It is very cheap, and is the easiest propellant to make on Mars. For over a quarter century, I have been a strong advocate of this design approach, making it a central feature of the Mars Direct mission architecture I first laid out in 1990 and described in my book The Case for Mars. However, it should be noted that while the manufacture of methane/oxygen from Martian carbon dioxide and water is certainly feasible, it is not without cost in effort, power, and capital facilities, and so the transportation system should be designed to keep this burden on the Mars base within manageable bounds.
3. The large scale manufacture of methane/oxygen bipropellant on the Martian surface from indigenous materials. Here I offer the same praise and the same note of caution as above. The use of in situ (that is, onsite) Martian resources makes the entire SpaceX plan possible, just as it is a central feature of my Mars Direct plan. But the scale of the entire mission architecture must be balanced with the production capacity that can realistically be established.
4. All flight systems are completely reusable. This is an important goal for minimizing costs, and SpaceX is already making substantial advances toward it by demonstrating the return and reuse of the first stage of its Falcon 9 launch vehicle. However, for a mission component to be considered reusable it doesnt necessarily need to be returned to Earth and launched again. In general, it can make more sense to find other ways to reuse components off Earth that are already in orbit or beyond. This idea is reflected in some parts of the new SpaceX plan such as refilling the second stage in low Earth orbit but, as we shall see, it is ignored elsewhere, at considerable cost to program effectiveness. Furthermore the rate at which systems can be reused must also be considered.
5. Refilling methane/oxygen propellant in the booster second stage in Earth orbit. Here Musk and his colleagues face a technical challenge, since transferring cryogenic fluids in zero gravity has never been done. The problem is that in zero gravity twophase mixtures float around with gas and liquid mixed and scattered among each other, making it difficult to operate pumps, while the ultracold nature of cryogenic fluids precludes the use of flexible bladders to effect the fluid transfer. However, I believe this is a solvable problem and one well worth solving, both for the benefits it offers this mission architecture and for different designs we may see in the future.
6. Use of the second stage to fly all the way to the Martian surface and back. This is a very bad idea. For one thing, it entails sending a 7millionpoundforce thrust engine, which would weigh about 60 tons, and its large and massive accompanying tankage all the way from low Earth orbit to the surface of Mars, and then sending them back, at great cost to mission payload and at great burden to Mars basepropellant production facilities. Furthermore, it means that this very large and expensive piece of capital equipment can be used only once every four years (since the feasible windows for trips to and from Mars occur about every two years).
7. The sending of a large habitat on a roundtrip from Earth to Mars and back. This, too, is a very bad idea, because the habitat will get to be used only one way, once every four years. If we are building a Mars base or colonizing Mars, any large habitat sent to the planets surface should stay there so the colonists can use it for living quarters. Going to great expense to send a habitat to Mars only to return it to Earth empty makes no sense. Mars needs houses.
8. Quick trips to Mars. If we accept the optimistic estimates that Musk offered during his presentation, the SpaceX system would be capable of 115day (average) oneway trips from Earth to Mars, a somewhat faster journey than other proposed mission architectures. But the speedier trips impose a great cost on payload capability. And they raise the price tag, thereby undermining the architectures professed purpose colonizing Mars since the primary requirement for colonization is to reduce cost sufficiently to make emigration affordable. Lets do some backoftheenvelope calculations. Following the example of colonial America, lets pick as the affordability criterion the property liquidation of a middleclass household, or seven years pay for a working man (say about $300,000 in todays equivalent terms), a criterion with which Musk roughly concurs. Most middleclass householders would prefer to get to Mars in six months at the cost equivalent to one house instead of getting to Mars in four months at a cost equivalent to three houses. For immigrants, who will spend the rest of their lives on Mars, or even explorers who would spend 2.5 years on a round trip, the advantage of reaching Mars oneway in four months instead of six months is negligible and if shaving off two months would require a reduction in payload, meaning fewer provisions could be brought along, then the faster trip would be downright undesirable. Furthermore, the sixmonth transit is actually safer, because it is also the trajectory that loops back to Earth exactly two years after departure, so the Earth will be there to meet it. And trajectories involving faster flights to Mars will necessarily loop further out into space if the landing on Mars is aborted, and thus take longer than two years to get back to Earths orbit, making the freereturn backup abort trajectory impossible. The claim that the SpaceX plan would be capable of 60day (let alone 30day) oneway transits to Mars is not credible.
9. The use of supersonic retropropulsion to achieve landing on Mars. This is a breakthrough concept for landing large payloads, one that SpaceX has demonstrated successfully in landing the first stages of its Falcon 9 on Earth. Its feasibility for Mars has thus been demonstrated in principle. It should be noted, however, that SpaceX is now proposing to scale up the landing propulsion system by about a factor of 50 and employing such a landing techniques adds to the propulsive requirement of the mission, making the (unnecessary) goal of quick trips even harder to achieve.
Improving the SpaceX ITS Plan
Taking the above points into consideration, some corrections for the flaws in the current ITS plan immediately suggest themselves:
A. Instead of hauling the massive second stage of the launch vehicle all the way to Mars, the spacecraft should separate from it just before Earth escape. In this case, instead of flying all the way to Mars and back over 2.5 years, the second stage would fly out only about as far as the Moon, and return to aerobrake into Earth orbit a week after departure. If the refilling process could be done expeditiously, say in a week, it might thus be possible to use the second stage five times every mission opportunity (assuming a launch window of about two months), instead of once every other mission opportunity. This would increase the net use of the second stage propulsion system by a factor of 10, allowing five payloads to be delivered to Mars every opportunity using only one such system, instead of the ten required by the ITS baseline design. Without the giant second stage, the spaceship would then perform the remaining propulsive maneuver to fly to and land on Mars.
B. Instead of sending the very large hundredperson habitat back to Earth after landing it on Mars, it would stay on Mars, where it could be repurposed as a Mars surface habitat something that the settlers would surely find extremely useful. Its modest propulsive stage could be repurposed as a surfacetosurface longrange flight system, or scrapped to provide material to meet other needs of the people living on Mars. If the propulsive system must be sent back to Earth, it should return with only a small cabin for the pilots and such colonists as want to call it quits. Such a procedure would greatly increase the payload capability of the ITS system while reducing its propellantproduction burden on the Mars base.
C. As a result of not sending the very large second stage propulsion system to the Martian surface and not sending the large habitat back from the Martian surface, the total payload available to send oneway to Mars is greatly increased while the propellant production requirements on Mars would be greatly reduced.
D. The notion of sacrificing payload to achieve oneway average transit times substantially below six months should be abandoned. However, if the goal of quick trips is retained, then the corrections specified above would make it much more feasible, greatly increasing payload and decreasing trip time compared to what is possible with the original approach.
Changing the plan in the ways described above would greatly improve the performance of the ITS. This is because the ITS in its original form is not designed to achieve the mission of inexpensively sending colonists and payloads to Mars. Rather, it is designed to achieve the sciencefiction vision of the giant interplanetary spaceship. This is a fundamental mistake, although the temptation is understandable. (A similar visionary impulse influenced the design of NASAs space shuttle, with significant disadvantage to its performance as an Earthtoorbit payload delivery system.) The central requirement of human Mars missions is not to create or operate giant spaceships. Rather, it is to send payloads from Earth to Mars capable of supporting groups of people, and then to send back such payloads as are necessary.
To put it another way: The visionary goal might be to create spaceships, but the rational goal is to send payloads.
Alternative Versions of the SpaceX ITS Plan
To get a sense of some of the benefits that would come from making the changes I [Zubrin] outlined above, lets make some estimates. In the table below, I [Zubrin] compare six versions of the ITS plan, half based on the visionary form that Elon Musk sketched out (called the Original or O design in the table) and half incorporating the alterations I [Zubrin] have suggested (the Revised or R designs).
Our starting assumptions: The ship begins the mission in a circular low Earth orbit with an altitude of 350 kilometers and an associated orbital velocity of 7.7 kilometers per second (km/s). Escape velocity for such a ship would be 10.9 km/s, so applying a velocity change (DV) of 3 km/s would still keep it in a highly elliptical orbit bound to the Earth. Adding another 1.2 km/s would give its payload a perigee velocity of 12.1 km/s, sufficient to send it on a sixmonth trajectory to Mars, with a twoyear freereturn option to Earth. (In calculating trip times to Mars, we assume average mission opportunities. In practice some would reach Mars sooner, some later, depending on the launch year, but all would maintain the twoyear free return.) We assume a further 1.3 km/s to be required for midcourse corrections and landing using supersonic retropropulsion. For direct return to Earth from the Martian surface, we assume a total velocity change of 6.6 km/s to be required. In all cases, an exhaust velocity of 3.74 km/s (that is, a specific impulse of 382 s) for the methane/oxygen propulsion, and a mass of 2 tons of habitat mass per passenger are assumed. A maximum booster secondstage tank capacity of 1,950 tons is assumed, in accordance with the design data in Musks presentation.
Using the improved plan to send 40 tons (3.3 times more) to Mars with Falcon Heavy
Consider what this revised version of the ITS plan would look like in practice, if it were used not for settling Mars but for the nearerathand task of exploring Mars. If a SpaceX Falcon Heavy launch vehicle were used to send payloads directly from Earth, it could land only about 12 tons on Mars. (This is roughly what SpaceX is planning on doing in an unmanned Red Dragon mission as soon as 2018.) While it is possible to design a minimal manned Mars expedition around such a limited payload capability, such mission plans are suboptimal. But if instead, following the ITS concept, the upper stage of the Falcon Heavy booster were refueled in low Earth orbit, it could be used to land as much as 40 tons on Mars, which would suffice for an excellent human exploration mission. Thus, if booster second stages can be refilled in orbit, the size of the launch vehicle required for a small Mars exploration mission could be reduced by about a factor of three.
In all of the ITS variants discussed here, the entire flight hardware set would be fully reusable, enabling lowcost support of a permanent and growing Mars base. However, complete reusability is not a requirement for the initial exploration missions to Mars; it could be phased in as technological abilities improved. Furthermore, while the Falcon Heavy as currently designed uses kerosene/oxygen propulsion in all stages, not methane/oxygen, in the revised ITS plan laid out above only the propulsion system in the transMars ship needs to be methane/oxygen, while both stages of the booster can use any sort of propellant. This makes the problem of refilling the second stage on orbit much simpler, because kerosene is not cryogenic, and thus can be transferred in zero gravity using flexible bladders, while liquid oxygen is paramagnetic, and so can be settled on the pumps side of the tank using magnets.
Dawn of the Spaceplanes
Toward the end of his presentation, Musk briefly suggested that one way to fund the development of the ITS might be to use it as a system for rapid, longdistance, pointtopoint travel on Earth. This is actually a very exciting possibility, although I would add the qualifier that such a system would not be the ITS as described, but a scaleddown related system, one adapted to the terrestrial travel application.
For a rocketplane to travel halfway around the world would require a DV of about 7 km/s (6 km/s in physical velocity, and 1 km/s in liftoff gravity and drag losses). Assuming methane/oxygen propellant with an exhaust velocity of 3.4 km/s (it would be lower for a rocketplane than for a space vehicle, because exhaust velocity is reduced by surrounding air), such a vehicle, if designed as a single stage, would need to have a mass ratio of about 8, which means that only 12 percent of its takeoff mass could be solid material, accounting for all structures, while the rest would be propellant. On the other hand, if the rocketplane were boosted toward space by a reusable first stage that accomplished the first 3 km/s of the required DV, the flight vehicle would only need a mass ratio of about 3, allowing 34 percent of it to be structure. This reduction of the propellanttostructure ratio from 7:1 down to 2:1 is the difference between a feasible system and an infeasible one.
In short, what Musk has done by making reusable first stages a reality is to make rocketplanes possible. But there is no need to wait for 500tontoorbit transports. In fact, his Falcon 9 reusable first stage, which is already in operation, could enable globespanning rocketplanes with capacities comparable to the DC3, while the planned Falcon Heavy (or New Glenn) launch vehicles could make possible rocketplanes with the capacity of a Boeing 737.
Nextbigfuture notes that reusable first stages are now technically functioning but safety and reliability would need to be improved by about 1000 to 10,000 times for point to point manned travel.
SOURCES Spacex, Zubrin, the New Atlantis
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Trump may fund the Spacex Mars Colonization plan – Next Big Future
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Golden ratio – Wikipedia
Posted: December 30, 2016 at 4:08 pm
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a>b>0,
where the Greek letter phi ( {displaystyle varphi } or {displaystyle phi } ) represents the golden ratio. Its value is:
The golden ratio is also called the golden mean or golden section (Latin: sectio aurea).[1][2][3] Other names include extreme and mean ratio,[4]medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8]
Some twentiethcentury artists and architects, including Le Corbusier and Dal, have proportioned their works to approximate the golden ratioespecially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratiobelieving this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.
Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as manmade systems such as financial markets, in some cases based on dubious fits to data.[9]
Two quantities a and b are said to be in the golden ratio if
One method for finding the value of is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/,
Therefore,
Multiplying by gives
which can be rearranged to
Using the quadratic formula, two solutions are obtained:
and
Because is the ratio between positive quantities is necessarily positive:
This derivation can also be found with a compassandstraightedge construction:
The golden ratio has been claimed to have held a special fascination for at least 2,400 years, though without reliable evidence.[11] According to Mario Livio:
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to presentday scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.[12]
Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into “extreme and mean ratio” (the golden section) is important in the geometry of regular pentagrams and pentagons. Euclid’s Elements (Greek: ) provides the first known written definition of what is now called the golden ratio: “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”[13] Euclid explains a construction for cutting (sectioning) a line “in extreme and mean ratio”, i.e., the golden ratio.[14] Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio.[15]
The golden ratio is explored in Luca Pacioli’s book De divina proportione of 1509.
The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as “about 0.6180340”, was written in 1597 by Michael Maestlin of the University of Tbingen in a letter to his former student Johannes Kepler.[16]
Since the 20th century, the golden ratio has been represented by the Greek letter (phi, after Phidias, a sculptor who is said to have employed it) or less commonly by (tau, the first letter of the ancient Greek root meaning cut).[1][17]
Timeline according to Priya Hemenway:[18]
De Divina Proportione, a threevolume work by Luca Pacioli, was published in 1509. Pacioli, a Franciscan friar, was known mostly as a mathematician, but he was also trained and keenly interested in art. De Divina Proportione explored the mathematics of the golden ratio. Though it is often said that Pacioli advocated the golden ratio’s application to yield pleasing, harmonious proportions, Livio points out that the interpretation has been traced to an error in 1799, and that Pacioli actually advocated the Vitruvian system of rational proportions.[1] Pacioli also saw Catholic religious significance in the ratio, which led to his work’s title. De Divina Proportione contains illustrations of regular solids by Leonardo da Vinci, Pacioli’s longtime friend and collaborator.
The Parthenon’s faade as well as elements of its faade and elsewhere are said by some to be circumscribed by golden rectangles.[25] Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, Midhat J. Gazal says, “It was not until Euclid, however, that the golden ratio’s mathematical properties were studied. In the Elements (308 BC) the Greek mathematician merely regarded that number as an interesting irrational number, in connection with the middle and extreme ratios. Its occurrence in regular pentagons and decagons was duly observed, as well as in the dodecahedron (a regular polyhedron whose twelve faces are regular pentagons). It is indeed exemplary that the great Euclid, contrary to generations of mystics who followed, would soberly treat that number for what it is, without attaching to it other than its factual properties.”[26] And Keith Devlin says, “Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation. The one thing we know for sure is that Euclid, in his famous textbook Elements, written around 300 BC, showed how to calculate its value.”[27] Later sources like Vitruvius exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.
A 2004 geometrical analysis of earlier research into the Great Mosque of Kairouan reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz.[28] They found ratios close to the golden ratio in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. The authors note, however, that the areas where ratios close to the golden ratio were found are not part of the original construction, and theorize that these elements were added in a reconstruction.
The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier’s faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as “rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned.”[29]
Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci’s “Vitruvian Man”, the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body’s height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. Le Corbusier’s 1927 Villa Stein in Garches exemplified the Modulor system’s application. The villa’s rectangular ground plan, elevation, and inner structure closely approximate golden rectangles.[30]
Another Swiss architect, Mario Botta, bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio, the golden ratio is the proportion between the central section and the side sections of the house.[31]
In a recent book, author Jason Elliot speculated that the golden ratio was used by the designers of the Naqshe Jahan Square and the adjacent Lotfollah mosque.[32]
Patrice Foutakis examined the measurements of 15 temples, 18 monumental tombs, 8 sarcophagi and 58 grave stelae from the fifth century BC to the second century AD. The temples were the main place for communication between the humans and Gods, while the tombs, sarcophagi and grave stelae were connected with the mortals’ passage from the material life to the eternal one. Should the golden ratio imply any divine, mystical or aesthetic property, then, according to the author, most of these constructions would be characterized by a goldensection rule. The result of this original research is that the golden ratio was totally absent from Greek architecture of the classical fifth century BC, and almost absent during the following six centuries. Four extremely rare and therefore valuable examples of goldenmean proportions were identified in an ancient tower in Modon (Peloponnese, Greece), in the Great Altar of Pergamon (Pergamon Museum, Berlin), in a grave stele from Edessa (Greece), and in a monumental tomb at Pella (Greece). Although these cases Foutakis claims to be evidence about a goldensection application in constructions of ancient Greece, he concludes that it was a marginal application indicating that the ancient Greeks did not pay any particular attention to the golden ratio as far as their architecture was concerned.[33]
The 16thcentury philosopher Heinrich Agrippa drew a man over a pentagram inside a circle, implying a relationship to the golden ratio.[2]
Leonardo da Vinci’s illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.[34] But the suggestion that his Mona Lisa, for example, employs golden ratio proportions, is not supported by anything in Leonardo’s own writings.[35] Similarly, although the Vitruvian Man is often[36] shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.[37]
Salvador Dal, influenced by the works of Matila Ghyka,[38] explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.[1][39]
Mondrian has been said to have used the golden section extensively in his geometrical paintings,[40] though other experts (including critic YveAlain Bois) have disputed this claim.[1]
A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is 1.34, with averages for individual artists ranging from 1.04 (Goya) to 1.46 (Bellini).[41] On the other hand, Pablo Tosto listed over 350 works by wellknown artists, including more than 100 which have canvasses with golden rectangle and root5 proportions, and others with proportions like root2, 3, 4, and 6.[42]
According to Jan Tschichold,[44]
There was a time when deviations from the truly beautiful page proportions 2:3, 1:3, and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter.
Some sources claim that the golden ratio is commonly used in everyday design, for example in the shapes of postcards, playing cards, posters, widescreen televisions, photographs, light switch plates and cars.[45][46][47][48][49]
Ern Lendvai analyzes Bla Bartk’s works as being based on two opposing systems, that of the golden ratio and the acoustic scale,[50] though other music scholars reject that analysis.[1] French composer Erik Satie used the golden ratio in several of his pieces, including Sonneries de la Rose+Croix. The golden ratio is also apparent in the organization of the sections in the music of Debussy’s Reflets dans l’eau (Reflections in Water), from Images (1st series, 1905), in which “the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position.”[51]
The musicologist Roy Howat has observed that the formal boundaries of La Mer correspond exactly to the golden section.[52] Trezise finds the intrinsic evidence “remarkable,” but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.[53]
Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.[54]
Though Heinz Bohlen proposed the nonoctaverepeating 833 cents scale based on combination tones, the tuning features relations based on the golden ratio. As a musical interval the ratio 1.618… is 833.090… cents (Play(helpinfo)).[55]
Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of parts such as leaves and branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these patterns in nature he saw the golden ratio operating as a universal law.[56][57] In connection with his scheme for goldenratiobased human body proportions, Zeising wrote in 1854 of a universal law “in which is contained the groundprinciple of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form.”[58]
In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.[59]
Since 1991, several researchers have proposed connections between the golden ratio and human genome DNA.[60][61][62]
However, some have argued that many apparent manifestations of the golden ratio in nature, especially in regard to animal dimensions, are fictitious.[63]
The golden ratio is key to the golden section search.
Studies by psychologists, starting with Fechner, have been devised to test the idea that the golden ratio plays a role in human perception of beauty. While Fechner found a preference for rectangle ratios centered on the golden ratio, later attempts to carefully test such a hypothesis have been, at best, inconclusive.[1][64]
The golden ratio is an irrational number. Below are two short proofs of irrationality:
Recall that:
If we call the whole n and the longer part m, then the second statement above becomes
or, algebraically
To say that is rational means that is a fraction n/m where n and m are integers. We may take n/m to be in lowest terms and n and m to be positive. But if n/m is in lowest terms, then the identity labeled (*) above says m/(nm) is in still lower terms. That is a contradiction that follows from the assumption that is rational.
Another short proofperhaps more commonly knownof the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. If 1 + 5 2 {displaystyle textstyle {frac {1+{sqrt {5}}}{2}}} is rational, then 2 ( 1 + 5 2 ) 1 = 5 {displaystyle textstyle 2left({frac {1+{sqrt {5}}}{2}}right)1={sqrt {5}}} is also rational, which is a contradiction if it is already known that the square root of a nonsquare natural number is irrational.
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial
Having degree 2, this polynomial actually has two roots, the other being the golden ratio conjugate.
The conjugate root to the minimal polynomial x2 – x – 1 is
The absolute value of this quantity ( 0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate.[10] It is denoted here by the capital Phi ( {displaystyle Phi } ):
Alternatively, {displaystyle Phi } can be expressed as
This illustrates the unique property of the golden ratio among positive numbers, that
or its inverse:
This means 0.61803…:1 = 1:1.61803….
The formula = 1 + 1/ can be expanded recursively to obtain a continued fraction for the golden ratio:[65]
and its reciprocal:
The convergents of these continued fractions (1/1, 2/1, 3/2, 5/3, 8/5, 13/8, …, or 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, …) are ratios of successive Fibonacci numbers.
The equation 2 = 1 + likewise produces the continued square root, or infinite surd, form:
An infinite series can be derived to express phi:[66]
Also:
These correspond to the fact that the length of the diagonal of a regular pentagon is times the length of its side, and similar relations in a pentagram.
The number turns up frequently in geometry, particularly in figures with pentagonal symmetry. The length of a regular pentagon’s diagonal is times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles.
There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution (see, for example, Thomson problem). However, a useful approximation results from dividing the sphere into parallel bands of equal surface area and placing one node in each band at longitudes spaced by a golden section of the circle, i.e. 360/ 222.5. This method was used to arrange the 1500 mirrors of the studentparticipatory satellite Starshine3.[67]
Application examples you can see in the articles Pentagon with a given side length, Decagon with given circumcircle and Decagon with a given side length.
The both above displayed different algorithms produce geometric constructions that divides a line segment into two line segments where the ratio of the longer to the shorter line segment is the golden ratio.
The golden triangle can be characterized as an isosceles triangle ABC with the property that bisecting the angle C produces a new triangle CXB which is a similar triangle to the original.
If angle BCX = , then XCA = because of the bisection, and CAB = because of the similar triangles; ABC = 2 from the original isosceles symmetry, and BXC = 2 by similarity. The angles in a triangle add up to 180, so 5 = 180, giving = 36. So the angles of the golden triangle are thus 367272. The angles of the remaining obtuse isosceles triangle AXC (sometimes called the golden gnomon) are 3636108.
Suppose XB has length 1, and we call BC length . Because of the isosceles triangles XC=XA and BC=XC, so these are also length. Length AC=AB, therefore equals +1. But triangle ABC is similar to triangle CXB, so AC/BC=BC/BX, AC/=/1, and so AC also equals 2. Thus 2 =+1, confirming that is indeed the golden ratio.
Similarly, the ratio of the area of the larger triangle AXC to the smaller CXB is equal to , while the inverse ratio is1.
In a regular pentagon the ratio between a side and a diagonal is {displaystyle Phi } (i.e. 1/), while intersecting diagonals section each other in the golden ratio.[8]
George Odom has given a remarkably simple construction for involving an equilateral triangle: if an equilateral triangle is inscribed in a circle and the line segment joining the midpoints of two sides is produced to intersect the circle in either of two points, then these three points are in golden proportion. This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H. S. M. Coxeter who published it in Odom’s name as a diagram in the American Mathematical Monthly accompanied by the single word “Behold!” [68]
The golden ratio plays an important role in the geometry of pentagrams. Each intersection of edges sections other edges in the golden ratio. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram’s center) is , as the fourcolor illustration shows.
The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is . The acute triangles are golden triangles. The obtuse isosceles triangles are golden gnomons.
The golden ratio properties of a regular pentagon can be confirmed by applying Ptolemy’s theorem to the quadrilateral formed by removing one of its vertices. If the quadrilateral’s long edge and diagonals are b, and short edges are a, then Ptolemy’s theorem gives b2=a2+ab which yields
Consider a triangle with sides of lengths a, b, and c in decreasing order. Define the “scalenity” of the triangle to be the smaller of the two ratios a/b and b/c. The scalenity is always less than and can be made as close as desired to .[69]
If the side lengths of a triangle form a geometric progression and are in the ratio 1: r: r2, where r is the common ratio, then r must lie in the range 1 1. A triangle whose sides are in the ratio 1: : is a right triangle (because 1 + = 2) known as a Kepler triangle.[70]
A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. In the rhombic triacontahedron the dihedral angle between any two adjacent rhombi is 144, which is twice the isosceles angle of a golden triangle and four times its most acute angle.[71]
The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:
The closedform expression for the Fibonacci sequence involves the golden ratio:
The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonaccilike sequence), as originally shown by Kepler:[20]
Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates ; e.g., 987/6101.6180327868852. These approximations are alternately lower and higher than , and converge on as the Fibonacci numbers increase, and:
More generally:
where above, the ratios of consecutive terms of the Fibonacci sequence, is a case when a = 1 {displaystyle a=1} .
Furthermore, the successive powers of obey the Fibonacci recurrence:
This identity allows any polynomial in to be reduced to a linear expression. For example:
The reduction to a linear expression can be accomplished in one step by using the relationship
where F k {displaystyle F_{k}} is the kth Fibonacci number.
However, this is no special property of , because polynomials in any solution x to a quadratic equation can be reduced in an analogous manner, by applying:
for given coefficients a, b such that x satisfies the equation. Even more generally, any rational function (with rational coefficients) of the root of an irreducible nthdegree polynomial over the rationals can be reduced to a polynomial of degree n 1. Phrased in terms of field theory, if is a root of an irreducible nthdegree polynomial, then Q ( ) {displaystyle mathbb {Q} (alpha )} has degree n over Q {displaystyle mathbb {Q} } , with basis { 1 , , , n 1 } {displaystyle {1,alpha ,dots ,alpha ^{n1}}} .
The golden ratio and inverse golden ratio = ( 1 5 ) / 2 {displaystyle varphi _{pm }=(1pm {sqrt {5}})/2} have a set of symmetries that preserve and interrelate them. They are both preserved by the fractional linear transformations x , 1 / ( 1 x ) , ( x 1 ) / x , {displaystyle x,1/(1x),(x1)/x,} this fact corresponds to the identity and the definition quadratic equation. Further, they are interchanged by the three maps 1 / x , 1 x , x / ( x 1 ) {displaystyle 1/x,1x,x/(x1)} they are reciprocals, symmetric about 1 / 2 {displaystyle 1/2} , and (projectively) symmetric about 2.
More deeply, these maps form a subgroup of the modular group PSL ( 2 , Z ) {displaystyle operatorname {PSL} (2,mathbf {Z} )} isomorphic to the symmetric group on 3 letters, S 3 , {displaystyle S_{3},} corresponding to the stabilizer of the set { 0 , 1 , } {displaystyle {0,1,infty }} of 3 standard points on the projective line, and the symmetries correspond to the quotient map S 3 S 2 {displaystyle S_{3}to S_{2}} the subgroup C 3
The golden ratio has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). It is, for that reason, one of the worst cases of Lagrange’s approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. This may be why angles close to the golden ratio often show up in phyllotaxis (the growth of plants).[72]
The defining quadratic polynomial and the conjugate relationship lead to decimal values that have their fractional part in common with :
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