The previous three post have been part of a series on geometric duality. The traditional but somewhat mysterious terminology is the pole of a line and the polar of a point. As explained here, the terminology was first coined in…
The previous two posts have been about polar triangles. The first used a polar triangle to derive a theorem, and the second showed how to compute polars using linear algebra. But what exactly is a polar triangle and why is…
So I've been familiar with the basics of polarization since forever, but I recently realized circular polarization is a mystery to me. I've heard of it in conjunction with eg satellite broadcasts, but I always thought it described aggregate behavior…
I’ve written before about the law of cosines on a sphere: But that’s just one of two laws of cosines on a sphere. The equation above is the law of cosines for sides. The law of cosines for angles is…
A buddy of mine had an interview and was asked some horrible interview question. He asked me about it afterward, but I wasn't any help. This has been bugging me all day and I couldn't find the solution on Google…
Topics: Staff, Math, Geometry, Biweekly Contest 23 You are given a circle represented as (radius, xCenter, yCenter) and an axis-aligned rectangle represented as (x1, y1, x2, y2), where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the…
Topics: Array, Math, Greedy, Sorting, Weekly Contest 119 Given an integer array nums, return the largest perimeter of a triangle with a non-zero area, formed from three of these lengths. If it is impossible to form any triangle of a non-zero…
Topics: Array, Math, Geometry, Weekly Contest 79 Given an array of points on the X-Y plane points where points[i] = [xi, yi], return the area of the largest triangle that can be formed by any three different points. Answers within 10-5 of…
Today's log begins with a question for Copilot.shu: This diagram was in a certain book. I believe it is likely a diagram related to geometric analysis, but since I have never received a proper explanation or known its original…
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Geometry: new shapes and polyhedra, geometric proofs and theorems, classic curves, and the geometers behind them.
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