What a blissful atmosphere at Maths Jam Antwerp yesterday, full of respect, encouragement and acceptance. It’s an international monthly meet-up taking place every second to last Tuesday of the month, simultaneously at many locations in the world, three hours of maths fun! This was Simon’s first time. He solved two difficult geometry problems and showed some of his current work to the math enthusiasts who attended. Was hopping and giggling all the way home.
Simon has crafted his own tiny slide rule that he carries around rolled up in an elastic band and calls his “toy”. The two strips of paper aligned together in certain ways can give answers to multiplication and division problems. Simon distributed the numbers on them according to a logarithmic scale.
Simon often drags his sketchbook to bed to “show me the beauty”, just before I would read a bedtime story to him and his sis. Last time he showed me a short proof of why there’re infinitely many primes. He assumed there were finitely many primes first… I think he learned that from James Grime:
Pi from Prime numbers:
Powers of 2:
Simon’s latest Live Stream about Chapter 6 of his “Living Code” Course (particle systems!), loosely based on Daniel Shiffman’s Nature of Code. “I’m also going to live stream a surprise maths video”, – at the beginning of the stream Simon devoted some time to the magic hexagon problem.
Simon wanted to make an outside video this afternoon, about what he’s been thinking of a lot lately – continued fractions. In the video below, he looks for curious number patterns while writing irrational numbers Phi and square root of 2 as their continued fractions. Partially inspired by Mathologer’s videos.
Square root of 2 expressed as its continued fraction:
The Golden Ratio (Phi) and the Fibonacci numbers:
Phi expressed as its continued fraction:
Simon has been watching a lot of Mathologer’s videos lately, mainly about Euler’s Number (e) and Pi. He is fascinated by the proofs Mathologer presented of why each number is irrational. “Mom, the proof that e is irrational actually doesn’t require any Calculus and the proof that Pi is irrational does! While you would expect it to be the other way around, right? Because e is about Calculus!”
Here are some of Simon’s notes, inspired by Mathologer. Some facts about e:
Notes about the proof that Pi is irrational:
Notes about the proof that e is irrational:
Simon watching the Mathologer channel:
Never a dull moment sitting down at a summertime terrace together with Simon. Just had a swim at the local pool and thought he was tired, but there he goes: Mom, I’ve got a game for you. Made these 9 cards and taught me how to play: each player grabs one card at a time and whoever has accumulated a valid sum or a set of three operators has won.
It was later that he showed me that the game is actually a number variant of tic tac toe and one should use the same strategy to get three in a row:
Simon and Neva make a 3D projection of a Hypertetrahedron – one of the regular solids in 4D – using straws. Simon looks up the formula for the center of the tetrahedron (radius of its circumscribed sphere) to measure the sides of the inside straws. To cut the exact length of the inside straws, he constructs a segment with the length of square root of six, divides it by 4 and multiplies the result by the original length of the straws.
Please also see our next and even cooler project – a 3D projection of a Hyperoctahedron:
The Hyperoctahedron came out to look very nice and four-dimensional. “It lands on the floor very nicely”, Simon says throwing it around – it is a very stable shape, made up of 16 tetrahedrons. Simon had to work out the centre of the triangle for this projection, which is easy to do for equilateral triangles.
The making of the Hyperoctahedron:
Measuring the center of the equilateral triangle:
Cutting the straws so that their length equals the distance between the vertex and the centre of the triangle:
The Hyperoctahedron is ready:
“I’m holding a four-dimensional shape in my hands!”
Looks like someone’s been studying a variety of bases…
Simon what is this, what are you making? – I was posh enough to make the tables of multiplications in base 12!