All posts tagged: geometry

Can’t whistle? It’s not you, it’s mouth geometry.

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy. You may unsubscribe at any time. There’s a video on YouTube, filmed back in 2019, where 100 random people try to whistle on camera. About half of them fail, often spectacularly. But partway through, the video flashes through the 50 or so who succeed, and something interesting jumps out: at a glance, every single one of them appears to be making the identical shape with their mouth. Look closely, and the shape is surprisingly specific. The lips pull back slightly at the corners, rather than pucker forward. A small, round opening is left in the middle: It’s closer to the width of a pencil than the wide “O” most people imagine. All of this raises an obvious question: If the ability to whistle really does require making a specific …

Monkeys are surprisingly good at geometry

Published by Jenni Sidey

Get the Popular Science daily newsletter💡 Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy. You may unsubscribe at any time. Only a handful of species apart from humans are known to understand geometry. It’s considered so rare among other animals that most scientists have long assumed even our closest non-human primate relatives struggle to grasp the concept of shapes and space. But according to a new study published today in the journal Proceedings of the National Academy of Sciences, some monkeys may not only have a solid handle on geometrical ideas—they cognitively process them in the same way as humans. “What surprised us wasn’t just that monkeys could do the task. It was that monkeys, children and adults seemed to think about geometric relationships in fundamentally the same way,” Jessica Cantlon, a study co-author, a cognitive neuroscientist at Carnegie Mellon University (CMU), explained …

Geometry, football and the World Cup final

Published by skeptic

Spain will play Argentina in the Fifa World Cup final on Sunday. The highly anticipated match takes place in New Jersey’s MetLife Stadium, with the teams vying for the most coveted prize in football. Attacking flair and physicality will no doubt play a role. But we could also see an underappreciated element of football come to the fore: geometry. In their 2-0 World Cup semi-final win over France, Spain formed neat passing triangles around the French players. This sometimes made it look as if Spain had extra people on the field. Wherever a Spanish player received the ball, two teammates appeared at different angles – with their French opponents seemingly always arriving a fraction too late. The triangle mattered not because it was neat, but because it gave Spain choice and France uncertainty. Each pass forced a French defender to commit to one possible future: press the ball, block the inside route, or protect the space behind. By the time that choice was made, the ball had often moved and the geometry had changed again. …

Chuck Jones’ The Dot and the Line Celebrates Geometry & Hard Work: An Oscar-Winning Animation (1965)

Published by José Betancourt

The animated short above, The Dot and the Line, directed by the great Chuck Jones and narrated by English actor Robert Morley, won an Oscar in 19656 for Best Animated Short Film. Based on a book written by Norton Juster, “The Dot and the Line” tells the story of a romance between two geometric shapes—taking the archetypal narrative trajectory of boy meets girl, loses girl, wins girl in the end (finding himself along the way) and injecting it with some fascinating social commentary that still resonates almost fifty years later. One way of watching “The Dot and the Line” is as a “triumph of the nerd” story, where an anxious square (as in “uncool”) Line has to compete with a hipster beatnik Squiggle of a rival for the affections of a flighty Dot. The Line begins the film “stiff as a stick… dull, conventional and repressed” (as his love interest says of him) in contrast to the groovy Squiggle and his groovy bebop soundtrack. With the possible suggestion that this love transgresses mid-century racial boundaries, the Line’s …

$A New AI Math Startup Just Cracked 4 Previously Unsolved Problems$

A New AI Math Startup Just Cracked 4 Previously Unsolved Problems

Published by skeptic

Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance along curved surfaces. While working on one theorem, they ran into an unexpected roadblock: Their argument depended on a strange formula from number theory, but they were unable to solve or justify it. In the end, Chen and Gendron wrote a paper presenting their idea as a conjecture, rather than a theorem. Chen recently spent hours prompting ChatGPT in the hopes of getting the AI to come up with a solution to the still unsolved problem, but it wasn’t working. Then, during a reception at a math conference in Washington, DC, last month, Chen ran into Ken Ono, a well-known mathematician who had recently left his job at the University of Virginia to join Axiom, an artificial intelligence startup cofounded by one of his mentees, Carina Hong. Chen told Ono about the problem, and the following morning, Ono presented him with a proof, courtesy of his startup’s …

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