Category Archives: Math

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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See, Accept, Affirm

The mathematical community is one, which—while not as diverse as it could/should be—counts as members individuals from all backgrounds and of all identities. These individualities are something we as a community should cherish and support. One outlet for such support … Continue reading

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What is a Manifold? (4/6)

After our luxurious treatment of 1-d manifolds, we turn to 2-d manifolds. My story of surfaces starts in a beautifully weird morning when I got up to realize that life in the usual Euclidean plane had changed dramatically. Vectors had shortened, areas … 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