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Tag Archives: Math
Optimal Control Theory to Settle Reinhardt’s Conjecture
The 2010’s are a Golden Age for packing problems. In 2014, Hales announced the longawaited completion of a highprofile machine proof project called FlySpeck, which verified his proof of Kepler’s conjecture. Johannes Kepler, in 1600, conjectured that the densest way to pack … Continue reading
Posted in General, Math
Tagged Control Theory, Math, Packing Problems, Reinhardt Conjecture, Sphere Packing
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What is a Manifold? (6/6)
In posts 13 we were able to reduce all of the geometry of a curve in 3space to an interval along with two or three realvalued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading
What is a Manifold? (5/6)
In our last post, we invented a new geometry by rescaling the inner product of the usual Euclidean plane. This modification did not change any of the angles in our geometry, in the sense that if two curves intersected in a particular Euclidean … Continue reading
Mathematical Democracy: Mission Impossible? Maybe not…
In 1950, a 29yearold PhD candidate at Columbia published a stunning theorem that later won him a Nobel Prize: “There is no such thing as a fair voting system.” Or so the legend goes. Let’s dive into this claim and … Continue reading
The Math of Elections
It seems like all anybody can talk about right now is the election. And while it has definitely given me a lot to think about in terms of political, cultural, and social problems in America, there’s also some interesting and potentially … Continue reading