Proving a Pythagorean triple. 3Blue1Brown did it in another way, using i.

# Tag: 3Blue1Brown

# Multiplying Complex Numbers in Processing

The math behind this project comes from the amazing math channel 3Blue1Brown: https://www.youtube.com/watch?v=QJYmyhnaaek

# Just another day in graphs

Simon loves looking at things geometrically. Even when solving word problems, he tends to see them as a graph. And naturally, since he started doing more math related to machine learning, graphs have occupied an even larger portion of his brain! Below are his notes in Microsoft Paint today (from memory):

Slope of Line:

Steepness of Curve:

An awesome calculator Simon discovered online at desmos.com/calculator that allows you to make mobile and static graphs:

Yesterday’s notes on the chi function (something he learned through 3Blue1Brown‘s videos on Taylor polynomials):

Simon following The Math of Intelligence course by Siraj Raval:

# 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.

# The Towers of Hanoi

Simon is a fan of the 3Blue1Brown channel and absolutely loved their video on solving the Towers of Hanoi puzzle with binary and ternary numbers. He practiced a lot with both. Eventually he developed his own, rhythmic, way to solve the puzzle:

Applying ternary numbers (solving the puzzle in 80 steps):

The video on 3Blue1Brown channel:

Applying binary numbers (solving the puzzle in 15 steps):

Simon watching 3Blue1Brown videos:

He also really liked the video on Visualizing the Riemann zeta function and yelled “Mom, look how beautiful this is!” the whole time:

Still from the 3Blue1Brown video that Simon found mesmerizing:

# Fractal Dimensions

Simon is talking about various shapes having various number of dimensions, which, oddly enough, doesn’t have to be a whole number. Based on maths tutorials on 3Blue1Brown channel, that Simon has been watching a lot over the past several days.