Creating figures with math software does not feel like fabricating illustrations for science posts. It is more of a meditation on geometry. I want to literally draw every line. I am not using grid lines or rendered surfaces. I craft a parametric curve for every line. A curve is set of equations. Yet, playing with … Continue reading Joys of Geometry
look at these towers Using the map creating a distorted image projected up to the sphere All connecting rays follow this rule Imaginary number i makes an appearance that borders on the poetic It’s nothing more than a whisper construct the proof for yourself something of a dying art avoid thinking about anything there has … Continue reading Elliptical Poetry
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 … Continue reading My Elliptical Cone
I poked at complex function 1/z, and its real and imaginary parts look like magical towers. When you look at these towers from above or below, you see sections of perfect circles. This is hinting at some underlying simplicity. Using the map 1/z, another complex number - w=1/z - is mapped to z. Four dimensions … Continue reading Lines and Circles
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 … Continue reading Mastering Geometry is a Lost Art
Chances are I made a fool of myself when trying to solve an intriguing math/physics puzzle described in this post. I wanted to create a German version but found it needs a revision. I will just give you my stream of consciousness as I cannot make it worse anyway. The puzzle presented by Quantum Boffin … Continue reading Revisiting the Enigma of the Intersecting Lines and That Pesky Triangle
On randomly searching for physics puzzles I have come across QuantumBoffin's site. The puzzle is about how to determine the center of mass of a body using the plumb line method, given there is some uncertainty due to experimental errors. You have found three plumb lines not intersecting in a single point; thus the three intersections of … Continue reading Physics / Math Puzzle: Where Is the Center of Mass?