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Modular Arithmetic visualized with Wheel Math

Simon learned this method from a MajorPrep video and was completely obsessed about it for a good couple of weeks, challenging everyone in our inner circle to factorize numbers using the wheels.

Simon’s proof for the 7 section circle. The remainders lie in the smallest circle (for example, the section where all the numbers are divisible by 7 have a zero in the inside circle, and in the section to the right you can see 1 in the inside i.e. all the numbers in this section mod 7 equal 1)
12 sections
5 sections
Coding, Java, Murderous Maths, Simon teaching, Simon's Own Code

28 times 28

Simon programmed a presentation to explain why 28×28 is not the same as 20×20 + 8×8 geometrically. The code is quite complicated and involves some trigonometry and conditional statements: the grid is divided into different parts every time Simon clicks and depending on how many times he has already clicked. This is typical Simon – coming up with an inherently arduous and complex system to visualise the beauty of the world around him, even of the seemingly trivial things. By the way, the inspiration for the 28×28 grid came from Simon’s favourite math channel, 3Blue1Brown and its latest video on Neural Networks (the grid was used to explain computer vision).

Simon is doing quite a lot of sums in his head nowadays, looks like it’s a new trend. Today, while bathing in the fountain outside, he was calculating how long 1/16th of a minute lasted. And a couple days ago, while waiting for his appointment at the hospital, he calculated how long it would take someone to read a whole page of random numbers, taking an educated guess that one takes 4 seconds to read out one number and remembering Daniel Shiffman mentioned there were 100×5 numbers per page in his book.

Murderous Maths

Graphic arithmetics

Simon is not only doing Precalculus en Calculus, but also enjoys maths at all levels (see previous post about The Secrets of Sums). For example, we do some Dutch elementary school tests to make sure he can handle the arithmetic. Below is a beautiful example of how his mind works. The task was to find the number exactly between 36×36 and 38×38 on the number line. Simon immediately came up with a parabolic graph and said it couldn’t be 37×37, based on that graph. I think he can graph just about anything in the world ­čÖé

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