geometry

Researchers have made a significant advance in spectral geometry by proving a special case of Pólya’s conjecture related to the eigenvalues of a disk. Their work, blending theoretical elegance with potential practical applications, highlights the universal value and artistic beauty of mathematical research. Credit: SciTechDaily.comA professor and his collaborators have proven Pólya’s conjecture for the eigenvalues of a disk, a tricky problem in mathematics.Is it possible to deduce the shape of a drum from the sounds it…

The “bullet heaven” genre was not something I seriously encountered until I started playing Vampire Survivors. It’s got that dopamine hit that comes when you’re the one the enemies have to watch out for. But if you want something that’s less about castles and spells and more about basic shapes in space, Geometry Survivor is where it’s at. As noted by Gaming on Linux, this is an upcoming rogue-like indie game with the timed, survival notions of something like Vampire Survivors, but with a look that’s closer to the…

This is today’s edition of The Download, our weekday newsletter that provides a daily dose of what’s going on in the world of technology. Exascale computers: 10 Breakthrough Technologies 2024 In May 2022, the global supercomputer rankings were shaken up by the launch of Frontier. It’s the fastest supercomputer in the world, and can perform as many calculations in one second as 100,000 laptops. With its launch, the era of exascale computing officially began. Several more such exascale computers will…

To train AlphaGeometry's language model, the researchers had to create their own training data to compensate for the scarcity of existing geometric data. They generated nearly half a billion random geometric diagrams and fed them to the symbolic engine. This engine analyzed each diagram and produced statements about their properties. These statements were organized into 100 million synthetic proofs to train the language model. Roman Yampolskiy, an associate professor of computer science and engineering at the University…

If you’ve never played Geometry Dash, you may find you’re missing out on one of the most engaging games in the rhythm genre. Now, after several years, not only has a new version been released, but it’s caused the concurrent player count to spike to an all-time high. According to recent data from SteamDB, Geometry Dash reached a peak of 88,346 on December 20. If you look at the graph, you can see how it shot up in the space of a couple of hours, with the previous count showing just under 13,000 players.…

Hidden amid its trademark satire of average American life, The Simpsons is riddled with mathematical Easter eggs. The show’s writing staff has boasted an impressive pedigree of Ivy League mathheads who couldn’t resist infusing America’s longest-running sitcom with inside jokes, scattered about like sprinkles on Homer’s doughnuts.The Hunger Games Director Francis Lawrence on Adapting a PrequelAs early as the opening shot of the show’s second episode, the perpetually one-year old baby, Maggie, stacks her alphabet blocks to…

In March, a group of mathematicians identified a thirteen-sided shape called “the hat” that can tile a surface without any patterns repeating. Now the researchers are updating the shape to maintain its quirky tiling properties while addressing an important caveat.Getty Images Wants AI to Stop Copying ThemThe new type of shape is called a “spectre” and it’s what’s known as an aperiodic monotile, which means that a single shape can tile a surface without any translational symmetry, or without its pattern ever repeating.…

Then last fall, Milman came up for sabbatical and decided to visit Neeman so the pair could make a concentrated push on the bubble problem. “During sabbatical it’s a good time to try high-risk, high-gain types of things,” Milman said.For the first few months, they got nowhere. Finally, they decided to give themselves a slightly easier task than Sullivan’s full conjecture. If you give your bubbles one extra dimension of breathing room, you get a bonus: The best bubble cluster will have mirror symmetry across a central…

Two high school students have proved the Pythagorean theorem in a way that one early 20th-century mathematician thought was impossible: using trigonometry. Calcea Johnson and Ne’Kiya Jackson, both at St. Mary’s Academy in New Orleans, announced their achievement last month at an American Mathematical Society meeting. “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that ... people don’t think that young people can do,” Johnson told WWL-TV, a New Orleans CBS…

We have the answer to Wordle (#657) on April 7, as well as some helpful hints to help you figure out the answer yourself right here. We’ve placed the answer right at the bottom of the page, so we don’t ruin the surprise before you’ve had a chance to work through the clues. So let’s dive in, starting with a reminder of yesterday’s answer. Yesterday’s Wordle answer Let’s start by first reminding ourselves of yesterday’s Wordle answer for those new to the game or who don’t play it daily, which was “leafy.” So we can say…