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Monthly Archives: November 2016
The Möbius function proof, part 1
In my last post, I introduced the Möbius function , which is defined in terms of the prime factorization of : if has any repeated prime factors, that is, if is divisible by a perfect square. Otherwise, if has distinct … Continue reading
The Möbius function
Time to pull back the curtain a bit! My recent series of posts on complex roots of unity may seem somewhat random and unmotivated so far, but the fact is that I definitely have a destination in mind—we are slowly … Continue reading
Computing sums of primitive roots
Remember this picture? It, and other pictures like it, express the fact that for a given , if we take the primitive roots for each of the divisors of , together they make up exactly the set of all th … Continue reading
Sums of primitive roots
In my previous post, we saw that adding up all the complex th roots of unity always yields zero (unless , in which case the sum is ). Intuitively, this is because the roots are symmetrically distributed around the unit … Continue reading
Sums and symmetry
Let’s continue our exploration of roots of unity. Recall that for any positive integer , there are complex numbers, evenly spaced around the unit circle, whose th power is equal to . These are called the th roots of unity. … Continue reading
Curvahedra
Everyone should go check out this Kickstarter project for CURVAHEDRA, a sort of construction kit that lets you build beautiful stuff like this: So cool! You can read more about the math behind them here. These are designed by Edmund … Continue reading
Posted in geometry, links
Tagged construction, Curvahedra, Kickstarter, polyhedra
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