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.

Today is one of the most beautiful days in Simon’s life: NYU Associate Professor and the creator of Coding Train Daniel Shiffman has been Simon’s guarding angel, role model and source of all the knowledge Simon has accumulated so far (in programming, math, community ethics and English), and today Simon got to meet him for the first time in real life!

Simon programmed this game a couple of weeks ago but I have waited to publish the video as I hoped he would finish it and get in on GitHub. Unfortunately he got stuck and didn’t return to the project since then, this why I’m now publishing an unfinished game. The unfinished code is on Simon’s GitHub: https://github.com/simon-tiger/muredo

Simon writes: “The game board is ready, you can move the game pieces on to the board and roll the die. As the next step, I want to have a feature of highlighting the correct tile – how can I do that?

I also don’t have the following things yet: the multiplying feature, choosing one of multiple options and the winning condition.”

I love Simon’s color choice and the whole interface. Originally, it’s a Japanese game and I think he has made it look very much like spring in Japan.

The objective of the game is to fill in the little square making a 3×3 grid. A player throws the dice and puts one game piece on the corresponding place on the board. When she throws again, she can multiply the value on the die by the value of the place where she has her game piece (or game pieces) if the product of the hat multiplication sum can be found among the nine numbers on the 3×3 grid. If not, the player either puts another game piece on the board, to fill the value of the last throw, or misses a turn.

As one of our Pi day activities, Simon attempted to calculate Pi by weighing a circle. In the video, you he first explains why this should work: the area of a circle with the radius r and the area of a square with a side of 2r can be expressed as Pi x r^2 and 4r^2 consecutively. This makes the ratio between the area of such a circle and the area of the square equal to Pi/4. In other words, Pi can be expressed as 4 times that ratio. But since both the circle and the square are made of the same material, their mass will also have the same ratio.

The result Simon got was pretty close, considering the low precision of our kitchen scales. As Simon’s math teacher correctly pointed out, the result would be much more precise if we had one thousand kids make their own circles and squares and weigh them, and then took the average of their outcomes.

Simon learned this trick from a Numberphile video. He made mental log sticks himself. He first programmed the nets in JavaScript and printed them out, then filled in the grids by hand. I helped him cut the grids out and glue them together. In the video, Simon uses the trick to quickly calculate the sum of four four-digit numbers and explains how he did it. If anyone wants to make these, here is a picture of the nets/grids:

Yesterday was Pi day and we are still celebrating! Simon experiments with calculating Pi with a physical thing, a pendulum. For the experiment, he cut a cord one fourth of the local gravity value (9.8m/s^2), that is 245 cm. One full swing of the cord makes Pi (measured in seconds)! Simon measures the time the pendulum makes 10 swings and divides that number by 10, to get the average duration of a swing.

The values Simon got were pretty close! The closest he got (not in this video, but later that day) was 3,128 sec., which is exactly the same value that Matt Parker got! What is the chance of that?

The formula is t = 2Pi times square root of l over g (where l is the length of the cord and g the local gravity).

Starring the cute 3Blue1Brown Pi. Here is some extra footage, with the 3Blue1Brown Pi riding the pendulum:

Simon came up with what he calls a conjecture about the minimum number of equilateral triangles that fit into a larger equilateral triangle. He has discovered that for equilateral triangles that have a length of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 the minimum number of equilateral triangles that fit into them is consecutively 4, 6, 4, 8, 4, 10, 4, 6, 4, 12, 4, i.e. a sequence with a repetitive pattern. In the two videos about Simon’s Triangles Conjecture, Simon explains this discovery and presents his proof. He supposes that the pattern continues for even larger triangles, but has proven it up to the side length of 12 so far.