The Best Shape for Train Wheels

Simon explains why train wheels are actually shaped like truncated cones. Inspired by a Numberphile video about stable rollers. The wooden slopes for the experiment Simon designed himself and his grandma (an ingenious craftswoman and woodworker, although a physician by profession) manufactured them for him.

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Trinity Hall Prime Number

Simon saw this pattern in a Numberphile video featuring Tadashi Tokieda and recreated it in Excel, adding colours. There are 30 columns and 45 rows of digits in this picture, which means it is made of 1350 digits – the year that Trinity Hall (in Cambridge) was founded. the bottom is all zeros, apart from a few glitches. The glitches were necessary because the whole thing (reading from right to left, top to bottom) is also one number and it is a prime number!

Trinity Hall Pime Number 4 Jul 2018

Tricks with paperclips and Knot Theory

Simon is pretty obsessed with Knot Theory at the moment (a mathematical theory that is widely used in advanced biology and chemistry, for example in handling tangled DNA).

He also learned a few tricks from one of his favourite teachers on Numberphile – Tadashi Tokieda – that probably also have something to do with Knot Theory. By folding a strip of paper in a certain way and placing rubber bands and paper clips on it and then pulling the ends of the paper strip, Simon gets the paper clips and the rubber bands linked together:

Making mathematical knots using rubber bands. A trefoil knot (the main prime knot):

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Simon says “it’s good for meditation”, too:

Irrationality of Square Roots

Simon has started a little video series about the Irrationality of Square Roots.

In Part 0, Simon talks about what square root of 2 is and in Part 1, he presents an algebraic proof that root 2 is irrational. He learned this from Numberphile.

In Part 2,┬áSimon presents a geometric proof that root 2 is irrational. Based on Mathologer’s videos.

Parts 3 and 4 following soon!

 

A new tour of Simon’s sketch book

The fertility formula, to predict the population the following year:

A fake number (called “Wau”) to imagine infinity (via Numberphile):

Drawing a square root of 5 (via James Grime):

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Pebbling a Chessboard (via Numberphile):

Kolakoski Sequence:

Proof for probabilities in a Wythoff’s game

Probability that everyone will be eliminated simultaneously in Simon’s “Hat Game” (a card game he invented):

Finite List of Primes:

Creating consecutive numbers by using various operators to connect four fours:

River Crossings Puzzle

This is a Japanese version of the famous River Crossings Puzzle that Simon learned from the Scam School channel (yes, our little programming and math nerd actually watches Scam School, a channel dedicated to social engineering at the bar and in the street!)

The answer, a sequence of 17 moves:

Simon showing the classic River Crossings puzzle to friends

Math graphs for solving the simple and the more advanced River Crossings puzzles using minimum vertex covers and Alcuin Numbers (learned via Numberphile):