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News
Here’s How Albert Einstein Proved Pythagoras Theorem When He Was 11
3+ week, 6+ day ago (31+ words) When looking through the book Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise by Manfred R. Schroeder, I came …...
The Transport Principle: Dividing by Zero in Geometric Algebra
1+ mon, 1+ week ago (1792+ words) The equations of gravity divide by zero at the centre of a black hole. This is the mathematics that refuses to stop there: no …...
Decades-old Problem In Classical Geometry Solved
6+ mon, 2+ hour ago (439+ words) Mirage News For over 150 years, a rule of thumb dating back to the French mathematician Pierre Ossian Bonnet has been accepted in surface theory: if the metric and mean curvature of a compact surface are known at every point, then…...
Trig of inverse trig
6+ mon, 2+ week ago (291+ words) I ran across an old article [1] that gave a sort of multiplication table for trig functions and inverse trig functions. Here’s my version of the table. I made a few changes from the original. First, I used LaTeX, which didn’t…...
Differential Geometry and Geometric Analysis
6+ mon, 3+ week ago (601+ words) The focus topic Differential Geometry and Geometric Analysis is closely related to topology, analysis, stochastics, group theory and to physic, e.g. Einstein's general relativity. A good background in algebra is helpful. Prerequisites for the specialization in differential geometry are the lecture…...
Hidden dimensions could explain where mass comes from
8+ mon, 4+ week ago (502+ words) The geometry of space itself may play a far more central role in physics than previously thought. Instead of serving only as the backdrop where forces act, spacetime may be responsible for the forces and particles that make up the…...
Which Science Degree is known as 'The Language of the Universe
9+ mon, 1+ week ago (382+ words) Mathematics is a vast discipline, broadly classified into pure mathematics (the study of concepts for their own sake) and Applied Mathematics (using concepts to solve real-world problems). The modern field is further organized into numerous specialized branches. Key Concepts & Areas…...
A circle in the hyperbolic plane
9+ mon, 2+ week ago (352+ words) Let ℍ be the upper half plane, the set of complex real numbers with positive imaginary part. When we measure distances the way we’ve discussed in the last couple posts, the geometry of ℍ is hyperbolic. What is a circle…...
Five formulas for the hyperbolic metric
9+ mon, 2+ week ago (329+ words) The previous post described a metric for the Poincaré upper half plane. The development is geometrical rather than analytical. There are also analytical formulas for the metric, at least four that I’ve seen. It’s not at all obvious that the…...
Cross ratio to define a metric on the hyperbolic plane
9+ mon, 2+ week ago (305+ words) One common model of the hyperbolic plane is the Poincaré upper half plane ℍ. This is the set of points in the complex plane with positive imaginary part. Straight lines are either vertical, a set of points with constant imaginary…...