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A hyperbolic triangle with three cusps
9+ mon, 2+ week ago (236+ words) In spherical geometry, the interior angles of a triangle add up to more than π. And in fact you can determine the area of a spherical triangle by how much the angle sum exceeds π. On a sphere of radius…...
How Do You Take the Root of a Triangle?
1+ mon, 3+ week ago (36+ words) You’ve Never Heard of Triangular Roots. If this is your first time coming across the term “triangular roots,” then you are where I was six months …...
Figure 3. The quarter circle visualization for the calculation of c.
3+ mon, 2+ week ago (24+ words) The Tech Figure 3. The quarter circle visualization for the calculation of c....
Triangular analog of the squircle
4+ mon, 6+ day ago (165+ words) TimF left a comment on my guitar pick post saying the image was a “squircle-ish analog for an isosceles triangle.” That made me wonder what a more direct analog of the squircle might be for a triangle. A squircle is…...
Structure and symmetry
11+ mon, 2+ week ago (199+ words) The highest distinction for mathematics research in the UK, the London Mathematical Society’s (LMS) Whitehead Prize, was conferred upon theme member Alessandro Sisto in 2024, while the LMS Anne Bennet Prize was awarded to theme member Lotte Hollands in 2018. We have…...
Scientists Say: Symmetry
1+ week, 5+ day ago (596+ words) Repeating patterns in shapes build everything from snowflakes to the body plans of life By folding a piece of paper in half and cutting a shape — such as a heart — from both sides at once, you can make a shape…...
Approximating even functions by powers of cosine
4+ mon, 1+ week ago (221+ words) A couple days ago I wrote a post about turning a trick into a technique, finding another use for a clever way to construct simple, accurate approximations. I used as my example approximating the Bessel function J(x) with (1 + cos(x))/2. I…...
Inverse cosine
6+ mon, 16+ hour ago (294+ words) In the previous two posts, we looked at why Mathematica and SymPy did not simplify sinh(arccosh(x)) to √(x² − 1) as one might expect. After understanding why sinh(arccosh(x)) doesn’t simplify nicely, it’s natural to ask why sin(arccos(x)) does…...
THE TRAPEZOIDAL-PARALLELEPIPEDAL TRIANGLE
3+ week, 4+ day ago (28+ words) It had always been just a Triangle — a rigid, flat, two-dimensional shape on a graphic processor screen in an Austin laboratory. Three angles, three edges …...
Trig of inverse trig
6+ mon, 2+ week ago (291+ words) 1957), pp. 502–503. It’d be interesting to see a similar table for cosh, sinh, and tanh, especially since...