The Wallace-Bolyai-Gerwien theorem states that any two polygons are equidecomposable: it is possible to cut any polygon into finitely many polygonal pieces and then rearrange them to obtain any other polygon.
The theorem doesn’t rely on the axiom of choice (unlike, for example, the more famous Banach-Tarski decomposition). Moreover, the decomposition and rearrangement (which consists of rotations and translations only) can by carried out “physically”: the pieces can, in theory, be cut with scissors from paper and reassembled by hand.
The problem about whether a hinged dissection exists, such as the ones in the animation, remained open until 2007. The paper Hinged Dissections Exist presents a method which always works to find a hinged dissection.
Fractal Beauty Beyond Belief -
Wakaya – Octorals & Giants, a stunning exhibition featuring Joshua Boger’s photographs from the deep sea and RISD’s electron micrographs, is on view in the Waterman 2nd Floor Gallery from Saturday, September 27 through Friday, October 3.
Simultaneously, the Nature Lab is hosting Beneath…
List of Universities on Tumblr -
Last updated: July 1st, 2014 with University of San Francisco, Austin Peay State University, University of New Mexico, George Mason University, and University of Alberta.
This is a running list of universities and university units on Tumblr, in alphabetical order. As far as I can tell, all these…
The Solution to ISIS Is the First Amendment -
As the elite panic about ISIS continues apace, it’s worth looking at how violations of the First Amendment have allowed …
You attract the right things when you have a sense of who you are. — Amy Poehler
(Source: splitterherzen, via elige)
How Memorizing "$19.05" Can Help You Outsmart the MTA -
We’ve all been there. The train is coming into the station, and you grab your MetroCard and quickly try and swipe it at a turnstile.
"Please Swipe Again". "Please Swipe Again". "Insufficient Fare".
The last two words are killer. You think to yourself “I swear I had a balance on this card”….
(Source: game-set-blog, via nadalrafa)
If I were killed by police today, which picture would they use? #IfTheyGunnedMeDown #WhichPictureWouldTheyUse
How Funny-Looking Benedict Cumberbatch Conquered Hollywood
The French have an expression called jolie laide—directly translated, it means “beautiful ugly,” but as a concept it embodies the intersection between attractiveness and unconventionality that makes us relish imperfection. Jolie laide is Sarah Jessica Parker and Benicio del Toro and Jessica Paré. It’s why Solange is visually more intriguing than Beyoncé, and why Meat Loaf, however improbably, was a sex symbol for much of the 1980s.
Sofia Coppola is often cited as the female embodiment of jolie laide, but as it relates to men, there’s no more obvious example in contemporary culture than Benedict Cumberbatch. In bleached-blonde, Botox-browed Hollywood, he’s the antithesis of everything we’re supposed to find attractive.
Read more. [Image: AP]
People ask me what I’m proudest of and what are my biggest frustrations as President. My biggest frustration is that this society hasn’t been willing to take some basic steps to keep guns out of the hands of people who can do damage. We’re the only developed country where this happens. And it happens weekly. Our levels of gun violence are off the charts. — President Obama sharing the difficulties of trying to change a culture in which school shootings are commonplace. (via whitehouse)
(Source: chels, via whitehouse)
Did you miss it? Watch today’s Tumblr Q&A right here to see President Obama answer questions on education, college affordability, and more.