Monthly Archives: January 2017

Dirichlet generating functions

Posted on January 30, 2017 by Brent

Suppose is a function defined for positive integers . Then we can define an infinite series as follows: (This might look a bit strange, but bear with me!) For example, suppose for all . Then (Note that in this case, … Continue reading →

Posted in number theory | Tagged , , , , , , , | 5 Comments

More fun with Dirichlet convolution

Posted on January 5, 2017 by Brent

I’m back after a bit of a hiatus for the holidays! Last time we saw how the principle of Möbius inversion arises from considering the function from the point of view of Dirichlet convolution. Put simply, the Möbius function is … Continue reading →

Posted in number theory | Tagged , , , , , , | 1 Comment

Paper torus with Villarceau circles

Posted on January 3, 2017 by Brent

I made another thing! This is a torus, made from 24 crescent-shaped pieces of paper with slots cut into them so they interlock with each other. I followed these instructions on cutoutfoldup.com. There is also a template with some ideas … Continue reading →

Posted in geometry | Tagged , , , , , | Comments Off on Paper torus with Villarceau circles