Simon saw this proof on the Numberphile channel.

# Tag: Numberphile

# Happy not back to school

Simon and Neva work on the math problem called ‘The Dollar Game’ late in the evening before the day school officially starts in Belgium and continue as soon as they wake up the following morning:

# 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.

# 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!

# 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):

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

# The three stated of matter (plasma not included)

Inspired by a Numberphile video with Tadashi Tokieda.

# Circle passing through a smaller square

Simon made a remix of the Numberphile video called “Round Peg in a Square Hole” (by Tadashi Tokieda) and worked out the albraic formula behind the trick.

# Convex vs. Concave Mirror

Simon learned this from Tadashi Tokieda in a Numberphile video called “Reflected Cats” and recreated the experiment.

# 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, Simon presents a geometric proof that root 2 is irrational. Based on Mathologer’s videos.

Parts 3 and 4 following soon!

# Different bases

Looks like someone’s been studying a variety of bases…