Geometry Joys, Murderous Maths

Parabolas are special

At the bakery, Simon tells me: “Parabola is the only shape that’s both an ellipse and a hyperbola (at least in a projective plane, which means that you can have a point at infinity). There are three ways to draw a parabola:

1. Graph y =x^2

2. Slice a cone parallel to its slope.

3. (Which we don’t really care about) Throw something.”

We buy modeling clay on the way home. He tries to reconstruct what he said about a parabola as a cross section of a cone.

Geometry Joys, Milestones, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

Geometric Definition of e

The idea comes from a video by Mathologer. Simon sketches a geometric definition of the Euler’s number (e) using integrals. He messed up a little with the integral notation, but corrected it later (after we stopped filming). Please see the photos below: