Coding, Geometry Joys, JavaScript, Milestones, Murderous Maths, Simon teaching, Simon's Own Code, Simon's sketch book

Space-filling Curves in p5.js.

Simon prepared this project as a community contribution for The Coding Train (Simon came up with his own way to draw the Hilbert Curve and added interactive elements to enable the user to create other colourful space-filling curves (Hilbert Curve, Z-order Curve, Peano Curve and more!). You can see Daniel Shiffman’s Hilbert Curve tutorial and coding challenge on The Coding Train’s website (including a link to Simon’s contribution) via this link:

Interactive full-screen version, allowing you to change the seed and the grid size:


Screen shot of The Coding Train website with a link to Simon’s contribution
Geometry Joys, Murderous Maths, Simon teaching

Hyperbolic space

This is a model of hyperbolic space (7 triangles around a vertex). It’s an open problem of how far you can keep expanding your structure this way (possibly infinitely far, if you allow the surface to cross itself). Which is strange, because with 3, 4 or 5 triangles around a vertex you get a platonic solid, so you definitely can’t go on forever. If you put 6 triangles around a vertex, you end up tiling a plane, so you definitely can go on forever.

For 7 or more triangles, it’s this sort of saddle shape and we don’t know if we can go on forever. How far can you go even if you do it physically? Physically you’ll definitely end up not going on forever, but still interesting to see how far you can go.

Biology, Coding, Experiments, JavaScript, Milestones, Simon teaching, Simon's Own Code, Simon's sketch book

Evolving Creatures in p5.js

Simon’s latest independent coding project involved some biology lessons! He loves the channel Primer by Justin Helps and watched his evolution series many times, studying the rules for species’ survival and multiplication. This resulted in two interactive evolution simulations, in both of which Simon recreated the rules he learned. The first simulation doesn’t involve natural selection and is based on these two videos: Simulating Competition and Logistic Growth and Mutations and the First Replicators.

Full Screen interactive version:


Simon added natural selection in Part 2, based on Primer’s video Simulating Natural Selection (the code Simon wrote from scratch):

Full Screen interactive version:


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

Alternating series, a crafty solution.

What does this infinite sun converge to?
Cut the four L-shapes out…
Divide the central L-shape in four L-shapes and cut those out, too…
You can go on forever…
but it’s already clear at this step, that the sum converges to 2/3 (two of the three squares the original L-shape was made up of)

Simon learned this from an alternating series visualization by Think Twice.

Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Tricks, Murderous Maths, Simon teaching, Simon's sketch book

Area of a dodecagon without trigonometry

How do you find out the area of this dodecagon without using trig?
Rearrange the triangles to make…
Three squares! The area of the dodecagon with a radius r is equal to the area of three r-sided squares or 3r^2.
The formulas for other polygons. There seem to be no formulas for the heptagon, nonagon and hendecagon (without using trigonometry that is). Simon’s notes above also say that no polygon can possibly have an area equal to or larger than πr^2 (because that’s the area of a circle). A square is 2r^2, a dodecagon is 3r^2, and so no polygon is 4r^2.

Simon learned this from a visual mathematics video by Think Twice.

Experiments, Murderous Maths, Notes on everyday life, Simon makes gamez, Simon teaching

2048 Cookies

We devoted the beginning of January to a goofy stop-motion project: Simon and I baked 2048 cookies! No, we didn’t bake over two thousand cookies! We only baked and decorated a little over a hundred of them, Simon had calculated that that would be enough to play the 2048 game… with cookies. Simon came up with all the editing tricks to make this project work. In the video, he also explains his winning strategy and confesses he has made another attempt to program the game, without me knowing it. Apparently, that’s how he first came up with the idea to bake the cookies, by looking up pictures of 2048 while programming and stumbling upon this blog.

Here is a link to Simon’s previous attempt to program 2048, about a year ago (he got pretty far).

Simon calculated how many cookies we needed and came up with a colour scheme
chemistry, Crafty, motor skills, Notes on everyday life, Simon teaching

Messing with the Periodic table

I want to mess with the Periodic Table to see what arrangements I can put it in.

This is called the Wide Arrangement. There are aso a few other arrangements, like the Left Step Wide (or Loop) arrangement, various 3D arrangements (like the ones where you make sure any consecutive numbers are next to each other and it looks like a layered cake).

Although it would be even nicer if we moved H and He over there where they obviously belong.

Spiral periodic table with no gaps between consecutive elements.
You can put it on the top of the Christmas Tree!
Mendeleev’s Flower

Simon learned this from a Minute Physics video.

Crafty, Geometry Joys, Group, Milestones, motor skills, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

MathsJam Antwerp 18 December 2019

Simon had a wonderful time at MathsJam Antwerp again. One of the problems was something he was already familiar with – the puzzle about hanging a painting using two pegs so that it would definitely fall if one removes any of the two pegs. He explained the way to solve this problem in an abstract way (turning pegs into strings, using knot theory and compiling the algorithm). Later the same evening, he developed a new algorithm to solve the same problem for three pegs and successfully demonstrated the result on his own shoe laces. His solution was the most efficient/ elegant in the group and his enthusiasm was very catchy, the audience said.

In the video below, Simon at first fails to apply his solution correctly, but succeeds upon the second attempt:

Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Math Tricks, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

Some more miscellaneous impressions of Simon's math-related adventures

a math trick based on probability and proof (presented to me while putting his pyjamas on one December evening)
the first thing he wrote on his new mini-whiteboard after getting it for Sinterklaas
while reading Stephen Wolfram’s A New Kind of Science
area of a hexagon
finding proof for puzzle solution
generally doing a lot of math with his little sister, like calcdocus in this picture
teaching mathematical concepts and solving problems to entertain family and friends