I’ve still been thinking about this elliptical cone! It has been the main character in my geometric proof on stereographic projection mapping circles to circles. The idea has been to reduce a three-dimensional problem to a two-dimensional one, by noting that something has to be symmetric. A circle on a sphere is mapped to some…

# Tag: Geometrical Proof

## Circles to Circles

Using stereographic projection, you create a distorted image of the surface of a sphere, stretched out to cover an infinite plane. Each point on the sphere is mapped to a point in the equatorial plane by a projection ray starting at a pole of the sphere. Draw a circle on the sphere, e.g. by intersecting…

## Mastering Geometry is a Lost Art

I am trying to learn Quantum Field Theory the hard way: Alone and from textbooks. But there is something harder than the abstract math of advanced quantum physics: You can aim at comprehending ancient texts on physics. If you are an accomplished physicist, chemist or engineer – try to understand Sadi Carnot’s reasoning that was…