2+ week, 8+ hour ago   (1468+ words) For the first time, mathematicians have found an example of a compact doughnutlike surface (as seen above) that shares its local geometric information with another surface, despite having a completely different global structure. Imagine if our skies were always filled…...

3+ mon, 9+ hour ago   (706+ words) Standing in the middle of a field, we can easily forget that we live on a round planet. We're so small in comparison to the Earth that from our point of view, it looks flat. This new perspective allowed mathematicians…...

3+ mon, 1+ week ago   (973+ words) The Platonic solids that have six, eight, 12 and 20 sides can pass through themselves. Imagine you're holding two equal-size dice. Is it possible to bore a tunnel through one die that's big enough for the other to slide through? Perhaps your…...

3+ mon, 4+ week ago   (1603+ words) The amplituhedron is a geometric shape with an almost mystical quality: Compute its volume, and you get the answer to a central calculation in physics about how particles interact. "Pasha has done some brilliant work related to the amplituhedron before,…...

4+ mon, 1+ week ago   (1422+ words) In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight. As mathematics advanced, the objects…...

8+ mon, 2+ week ago   (1892+ words) Geometry may have its origins thousands of years ago in ancient land surveying, but it has also had a surprising impact on modern physics. In the latest episode of The Joy of Why, Yang-Hui He explores geometry's evolution and its…...