geometry – Quanta Magazine https://www.quantamagazine.org Illuminating science Mon, 16 Sep 2024 14:10:47 -0400 en-US hourly 1 https://wordpress.org/?v=6.2 The Geometric Tool That Solved Einstein’s Relativity Problem https://www.quantamagazine.org/the-geometric-tool-that-solved-einsteins-relativity-problem-20240812/ https://www.quantamagazine.org/the-geometric-tool-that-solved-einsteins-relativity-problem-20240812/#respond Mon, 12 Aug 2024 14:49:08 +0000 https://www.quantamagazine.org/?p=139724 The post The Geometric Tool That Solved Einstein’s Relativity Problem first appeared on Quanta Magazine

]]> After Albert Einstein published his special theory of relativity in 1905, he spent the next decade trying to come up with a theory of gravity. But for years, he kept running up against a problem. He wanted to show that gravity is really a warping of the geometry of space-time caused by the presence of matter. But he also knew that time and distance are counterintuitively relative: They change...

Source

]]> https://www.quantamagazine.org/the-geometric-tool-that-solved-einsteins-relativity-problem-20240812/feed/ 0 Monumental Proof Settles Geometric Langlands Conjecture https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/ https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/#respond Fri, 19 Jul 2024 14:02:17 +0000 https://www.quantamagazine.org/?p=139195 The post Monumental Proof Settles Geometric Langlands Conjecture first appeared on Quanta Magazine

]]> A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said Peter Scholze, a prominent mathematician at the Max Planck Institute for Mathematics who was not involved in the proof. “It’s wonderful to see it resolved.

Source

]]> https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/feed/ 0 What Can Tiling Patterns Teach Us? https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/ https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/#respond Wed, 03 Jul 2024 13:20:01 +0000 https://www.quantamagazine.org/?p=138915 The post What Can Tiling Patterns Teach Us? first appeared on Quanta Magazine

]]> In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur victor. That discovery of the elusive aperiodic monotile propelled the field into new dimensions. The study of tessellation is much more than a fun thought exercise: Peculiar...

Source

]]> https://www.quantamagazine.org/what-can-tiling-patterns-teach-us-20240703/feed/ 0 Why Is This Shape So Terrible to Pack? https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/ https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/#respond Fri, 28 Jun 2024 14:42:22 +0000 https://www.quantamagazine.org/?p=138843 The post Why Is This Shape So Terrible to Pack? first appeared on Quanta Magazine

]]> For centuries, mathematicians suspected that hexagonal tiles are the best possible way to fill space. By this they mean that if you want to subdivide a large area into tiles of equal size while minimizing the perimeter of each tile, you can’t do any better than hexagons. In 1999, Thomas Hales of the University of Pittsburgh finally proved it. They’re better than squares, triangles...

Source

]]> https://www.quantamagazine.org/why-is-this-shape-so-terrible-to-pack-20240628/feed/ 0 Mathematicians Attempt to Glimpse Past the Big Bang https://www.quantamagazine.org/mathematicians-attempt-to-glimpse-past-the-big-bang-20240531/ https://www.quantamagazine.org/mathematicians-attempt-to-glimpse-past-the-big-bang-20240531/#respond Fri, 31 May 2024 14:08:57 +0000 https://www.quantamagazine.org/?p=138260 The post Mathematicians Attempt to Glimpse Past the Big Bang first appeared on Quanta Magazine

]]> About 13.8 billion years ago, the entire cosmos consisted of a tiny, hot, dense ball of energy that suddenly exploded. That’s how everything began, according to the standard scientific story of the Big Bang, a theory that first took shape in the 1920s. The story has been refined over the decades, most notably in the 1980s, when many cosmologists came to believe that in its first moments...

Source

]]> https://www.quantamagazine.org/mathematicians-attempt-to-glimpse-past-the-big-bang-20240531/feed/ 0