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 long-awaited completion of a high-profile 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

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What is a Manifold? (6/6)

In posts 1-3 we were able to reduce all of the geometry of a curve in 3-space to an interval along with two or three real-valued functions. We also discussed when two sets of such data give equivalent (overlapping) curves. This … Continue reading

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What is a Manifold? (5/6)

In our last post, we invented a new geometry by re-scaling 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

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Mathematical Democracy: Mission Impossible? Maybe not…

In 1950, a 29-year-old 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

Posted in Math, Math in Pop Culture, Mathematics in Society, Social Justice, Uncategorized, Voting Theory | Tagged , , , , | 3 Comments

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

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