Crafty, Geometry Joys, Math Tricks, Murderous Maths, Simon teaching, Simon's sketch book

Inscribed angle theorem

“It reveals itself once you complete the rectangle to find the centre. Because, of course, the diagonal passes through the centre once you inscribe a rectangle inside the circle, because of the symmetry”.
Tiling the quadrilaterals Simon has crafted applying the inscribed angle theorem.
Tiling the “shapes generated by the inscribed angle theorem”
“The theorem says that if you have a circle and just three random points on it, then you draw a path between te first point to the second, to the centre, to the third point and back to the first point”.
Coding, JavaScript, Murderous Maths, Physics, Simon teaching, Simon's Own Code, Simon's sketch book

Heat Equation Visualization

A visual solution to Fourier’s heat equation in p5. Play with the two versions online:
https://editor.p5js.org/simontiger/present/EaHr9886H
https://editor.p5js.org/simontiger/sketches/EaHr9886H

https://editor.p5js.org/simontiger/present/ruN8CQV77
https://editor.p5js.org/simontiger/sketches/ruN8CQV77

Inspired by 3Blue1Brown’s Differential Equations series.

Geometry Joys, Math Tricks, Murderous Maths, Simon teaching, Simon's sketch book

Triangular, Square, Pentagonal, Hexagonal Numbers

Applying one of his favorite materials – checkers – Simon showed me the tricks behind polygonal numbers. The numbers written in pen (above) correspond to the actual triangle number (red rod) and the row number (blue rod).
Square numbers
Pentagonal numbers
And the next pentagonal number
(Centered) Hexagonal numbers
Fragment of the next (centered) hexagonal number
The following morning I saw that Simon came up with these general formulae to construct square, pentagonal and hexagonal numbers using triangle numbers. The n stands for the index of the polygonal number. Later Simon told me that he had made a mistake in his formula for the hexagonal numbers: it should not be the ceiling function of (n-1)/2, but simply n-1, he said.

I asked Simon to show me how he’d come up with the formulae:

Here is a square number constructed of two triangle numbers (the 5th and the 4th, so the nth and the n-1st)
The working out of the same construction. In the axample above n equals 5, so the 5th square number is indeed 25.
The nth pentagonal number constructed using three triangle numbers: the nth triangle number, and two, n-1st triangle numbers.
The working out of the pentagonal number formula
The nth hexagonal number
The formula for calculating the nth hexagonal number from six n-1st triangle numbers plus 1. (Simon later corrected the (n+1) into (n-1)).
Coding, Math Riddles, Math Tricks, Murderous Maths, Python

Number Guessing Game

Simon writes: Made a little game where the computer thinks of a number 1-100, and you try to guess it within 7 takes! Hint: the algorithm is called “Binary Search”. https://repl.it/@simontiger/NumberGuessingGame
You can also play the fullscreen version here: https://numberguessinggame.simontiger.repl.run/

Now also a reversed version, where you think of a number and the computer guesses it: https://repl.it/@simontiger/BinaryNumGuessingGame

Group, Math Riddles, Murderous Maths, Notes on everyday life

MathsJam 18 June 2019

This was the last MathsJam this academic year and a very social one. Simon has enjoyed the outside setting and mingled with the other mathematicians.
Simon had also contributed two problems (numbers 3 and 5). Unfortunately we haven’t seen anyone solve them (the problems come from the Russian math olympiad published in the magazine Kvantik).
Simon had recognized two problems he knew the answers to. Here he is explaining the persistences problem (number 13).
The smallest number with persistence 5 is 679
Simon trying to prove that the solution to problem number 2 is e.
Math Riddles, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book, Together with sis

Teaching Mathematical Fundamentals

Simon loves challenging other people with math problems. Most often it’s his younger sister Neva who gets served a new portion of colourful riddles, but guests visiting our home also get their share, as do Simon’s Russian grandparents via FaceTime. Simon picks many of his teaching materials in the Mathematical Fundamentals course on Brilliant.org, and now Neva actually associates “fundamentals” with “fun”!

Crafty, Geometry Joys, motor skills, Murderous Maths, Simon teaching, Simon's sketch book

A Square Triangle?

Simon explains what Gaussian formula is to check a shape’s curvature and shows how to make a triangle with three 90° angles. Or is it a square, since it’s a shape with all sides equal and all angles at 90°? He also says a few words about the curvature of the Universe we live in.

Almost everything he shares in this video Simon has learned from Cliff Stoll on Numberphile:
https://www.youtube.com/watch?v=n7GYYerlQWs
https://www.youtube.com/watch?v=gi-TBlh44gY