Assaf Bar-Natan.
Is there food at fields right now?

This is a picture of me. It is not relevant to my research.

Hi! This is my page. There are many others like it, but this one is mine. I am currently using this website to host silly scripts that I sometimes want to send to people:

During the summer of 2018, I biked from Toronto to Boston, and wrote a blog about it.
Here's a link
Later, I biked from Boston to Montreal.
Here's a link
Random Generators
This is a picture of something that is relevant to my MsC research.

A circular kingdom named Amestris wants to promote tourism, and decides to build scenic roller-coasters that will start and end at the borders of Amestris and circulate through its n monuments. However, the queen of Amestris wants the different roller coasters to go along different routes, and she does not want to build too many bridges, so she imposes the following rules
  • No two roller coaster tracks can be parallel from start to finish. That is, there are no strips of land devoid of monuments between any two roller coaster tracks.
  • Any two roller coasters can only cross each other twice
The queen asks the court mathematician how many roller coasters she can build. As the court mathematician, this is the problem I am working on right now. I know the answer. Do you? Can you find the answer for n=2? n=3? n=4? Can you guess the pattern?
Hint: If you trace out lines which go from the edge of the picture, through the opposite edges of each square in the pictures below, you get the answers for n=2,3,4,5. Count the lines you drew, and try to find a pattern (Look at Pascal's triangle)!