Projective Geometry of Elliptic and Quadratic Curves

Parabolas, circles, and hyperbolas may look vastly different on a graph, but there is a way to paint these pictures on a ball such that they all turn into circles? It turns out that all quadratic curves turn into circles, and we can see this by copying a graph onto a balloon. What happens to other curves when we put them on a balloon?

Videos:

• YouTube video explaining the math behind perspective drawings
  • https://www.youtube.com/watch?v=mTw3o8-xMIo

Additional Resources:

• A Brilliant.org article describing projective geometry
  • https://brilliant.org/wiki/projective-geometry/

Technical Resources:

• A chapter of a book by Jean Gallier describing the algebra behind projective geometry:
  • https://www.cis.upenn.edu/~jean/gma-v2-chap5.pdf
• An article by Michael Logal about elliptic curves:
  • https://used1brain.github.io/long_boi_paper.pdf