This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
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: https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html
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.
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.
For over a month, Simon has been fascinated by Presh Talwalkar’s channel Mind Your Decisions. The channel is full of short videos on famous math problems, logic riddles, proofs and mental math tricks. Simon has also ordered a compilation of Talwalkar’s five most interesting books, including “The Joy of Game Theory: An Introduction to Strategic Thinking”, that we are currently very much enjoying together, and four more, that Simon is reading on his own: “40 Paradoxes in Logic, Probability, and Game Theory”, “The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias”, “The Best Mental Math Tricks”, and “Multiply Numbers By Drawing Lines”.
This one became Simon’s favourite brain teaser. It sounds like it’s filled with irrelevant information, but somewhat counterintuitively, every little bit of information in this puzzle helps! Here is the puzzle: A mathematician tells a census taker he has 3 children. The product of their ages is 72 and the sum of their ages is the house number. The census taker tries to figure it out but explains he still does not know. The mathematician says, “Of course not. I forgot to tell you my oldest child loves chocolate chip cookies.” Now the census taker figures it out. What are the ages of the children?
Simon has also picked up many nifty tricks and beautiful magic squares, both from the book and from the YouTube channel.
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).
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.
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: