Setup It’s time for another geometry walkthrough motivated this week by this interesting problem from James Tanton. “Two isosceles right triangles are hinged at corners as shown. Line segment c...

This post starts with reading elsewhere about someone struggling with the following trig identity given a triangle with three angles x, y, z show: [\tan{x} + \tan{y} + \tan{z} = \tan{x}\cdot\tan{y...

Its been a long while since my last social media post: https://blog.mathoffthegrid.com/2017/08/how-i-use-twitter.html  and everything is all of a sudden in huge flux.  With all the turmoil on Twitt...

Source: @ElyemGercek I saw this post and immediately thought: “What an odd connection to Pascal’s Triangle. What’s going on?” Due to time constraints I didn’t get a chance to look into this for ...

What motivated this essay was two posts I recently saw. The first started with the idea that no student should take more than five minutes on a problem. If stuck it was unlikely to be productive an...

** ** **Graphic scores by John De Cesare (1890–1972). ** Welcome to the 203rd Carnival. For all the other carnivals future and past, visit The Aperiodical where you can also submit future posts....

I just saw a nice visual proof of the ratios for the 15-75-90 on the internet via @ilarrosac.   This one works via symmetry and the Pythagorean theorem. 

I really enjoyed working through this problem from Stanley Rabinowitz I saw recently on Twitter. This was one of those problems where I circled around it and after finding the first solution realiz...

Here’s a straightforward trigonometric proof of Ptolemy’s Theorem using scale factors and the Law of Cosines. First we start with a cyclic quadrilateral and assign it segment lengths: $ \triang...

What follows is a walkthrough of the problem above which I had a lot of fun playing around with. Most of the solutions I saw online used trigonometry and so just to be different I’m going to appr...