Tag: Geometrical Proof
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Proven Cone
Why are circles projected onto circles under stereographic projection? In 2021, I developed a geometrical proof I had not seen elsewhere. I have started from the observation that the circle on the sphere and its image are both connected by some sort of cone. What is the base area of this cone? If the cone…
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My Elliptical Cone
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…
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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…
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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…