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 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:
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!”
Simon what is this, what are you making? – I was posh enough to make the tables of multiplications in base 12!
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):
Pebbling a Chessboard (via Numberphile):
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:
Inspired by the videos by Matt Parker
and James Grime:
Simon also made the Borromean rings:
And cubes (which Simon now uses to practice juggling!)
In this live session, Simon continue my 15s puzzle redo live session (“yet again, but I swear this is going to be the last time I do this!” Simon said). Here’s a link to the previous part. This week’s live stream went great, Simon kept it concise, didn’t panic while debugging, largely thanks to a wonderful supportive audience. And he even got some interesting personal questions asked in the end!
This is Simon’s remix of a video by James Grime about the same subject on the SingingBanana math channel: https://www.youtube.com/watch?v=ODtwehGzoLM
The Utilities Problem is a problem about connecting three houses to three utility companies of which every company provides three services (water, gas, electricity) so that no lines cross.
Simon proves the problem impossible by contradiction (by assuming it’s possible and applying Euler’s Formula about 3D Solids to the solution).
Simon had quite an audience yesterday during his live lesson. In this week’s session, Simon remade his 15’s Puzzle in Processing and explained the math behind it. He plans to finish the puzzle during his next live stream in two weeks from now (on April 19 at 17:15 CET).
Simon talking about his Tantrix Game code and the math behind it. It has been Simon’s first community project, many thanks to everyone who has contributed hexagonal tiles for the game! The game isn’t finished yet, but the video gives a good insight into the work in progress. Simon will finish it at a later date he says. Feel free to try and finish it on your own and share your results! The code is on GitHub at: https://github.com/simon-tiger/tantrix
This is a separate link to see what Simon has got so far in action: https://simon-tiger.github.io/tantrix/tantrix/
Below is Simon’s original YouTube post summoning contributions: