This blog is about Simon, a young gifted programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool.

Simon came up with a tool (a circle where you install a pencil) to draw curved lines. He explains how the curved line actually draws the absolute value of the Sine function sin(x). “Because an absolute value of x is square root of x squared, that means that all negative values cancel out”, says Simon, that’s why the wave looks spiky.

Simon’s tool should probably be improved by making it from thicker material like thick cardboard.

What shape can roll well, other than a circle (wheel)? Two circles, attached together according to a formula involving a square root of two! Simon made these “wobbly circles” inspired by a Numberphile video where Matt Parker talks about how the ability to roll well (as in a wheel) is caused by the constant height of the center of mass (as opposed to a square wheel, whose center of mass goes zigzagging up and down). Wobbly wheels also have a stable height of their center of mass, hence they roll!

Simon also made a transparent version (with mom’s help):

Simon came up with an idea to make a puzzle of “squared squares”, a concept he learned via Numberphile. One square of 112 by 112 cm (the smallest possible of the squared squares) is made up of squares that each form a sum of two or more neighboring squares. Simon later completed the whole puzzle, together with his little sis. They had to pick up the tiniest square with a pair of tweezers!

Simon drew all the exact pieces of the puzzle on a sheet of paper first, but then – open source minded as he is – he decided to create a website where the pieces would be available for everyone to print out. We’ll post the link here once the website is online (I sometimes literally beg Simon to put projects online, as he always considers them unfinished or not good enough). He also wrote a webpage about the concept of squared squares, but (surprise!) hasn’t hosted it on GitHub yet either. Here comes a screenshot of the webpage:

As the last exercise with this concept, Simon also calculated the area of the smallest possible squared square on his desktop calculator:

Simon built this Tetris game in one day on Wednesday. He didn’t use any libraries. The code largely comes from a Meth Meth Method video tutorial, but Simon made it object oriented and adjusted some parameters.
You increase your score for every row that’s fully populated. However, if you have four rows that are almost fully populated and you get them fully populated at once, you increase your level.
Link to Simon’s code: https://github.com/simon-tiger/tetris-js

In case you wonder, what on earth are cellular automata:

A cellular automaton (pl. cellular automata, abbrev. CA) is studied in computer science, mathematics, physics, theoretical biology and microstructure modeling.

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off . The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function)^{} that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood.

The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway’s Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. Wolfram published A New Kind of Science in 2002, claiming that cellular automata have applications in many fields of science. These include computer processors and cryptography. (Wikipedia)

Simon shows the Cannon game he created in Processing (Java). He says he was inspired by the Stackoverflow forum, where he saw an example of the game and later wrote the code for a similar game himself. I saw him quickly write the code in a matter of perhaps two hours. Simon will post his code on GitHub once he has added a couple extra features.

We continue reading the Russian adventurous math books by Vladimir Levshin (1904-1984) – see an older post about it – and Simon is often excited about the challenges discussed. This time however, he first thought that something was impossible (and the Russian book said that, too), but our amazing favourite Murderous Math thought otherwise! It was one of the three oldest “unresolved” problems in the world, about how to double a cube (and let it remain a cube), which basically boils down to “how to draw the cube root of 2”:

Some more unrelated notes that Simon made recently, while listening to the Russian adventurous math book:

Digisnacks, an electronica course at Artesis Plantijn Hogeschool Antwerpen, has started again. This time it’s Lego Mindstorms 2. Simon didn’t follow the Lego Mindstorms 1 course but studied how the set works via a couple of YouTube tutorials. It’s a course for 10-14 olds 😉