Modular Arithmetic visualized with Wheel Math

Simon learned this method from a MajorPrep video and was completely obsessed about it for a good couple of weeks, challenging everyone in our inner circle to factorize numbers using the wheels.

Simon’s proof for the 7 section circle. The remainders lie in the smallest circle (for example, the section where all the numbers are divisible by 7 have a zero in the inside circle, and in the section to the right you can see 1 in the inside i.e. all the numbers in this section mod 7 equal 1)
12 sections
5 sections
Computer Science, Electronics, Engineering, Good Reads, Notes on everyday life, Uncategorized

The Digital Computer Electronics book

Simon has been mesmerised by this book for a couple of days by now, the Digital Computer Electronics eBook (third edition). He has downloaded it online and has been reading about the so called “simple as possible” processors or the sap’s (he loves the name) one of which is like the 8-bit computer he is currently trying to build from scratch.

Simon reading the book in the playroom. I hearbhim laughing and reading aloud.
a screenshot of the book
Taking notes on SAP-2 instructions (and listening to a quiz show on YouTube at the same time) – his way of learning
art, Coding, Crafty, Java, Milestones, Murderous Maths, Simon teaching, Simon's Own Code, Simon's sketch book, Uncategorized

Simon’s Times Tables Visualization is Now a Huge Poster!

Simon has made an enormous poster from his earlier animated version of the Times Tables Visualization! Simon is hoping to present this project at the Processing Community Day in Amsterdam in January 2019. The poster is already being printed!


Simon writes: This is a visualization for the times tables from 1 to 200.
Start with a circle with 200 points. Label the points from 0-199, then from 200-399, then from 400-599, and so on (you’re labeling the same point several times).

We’ll first do the 2x table. 2×1=2, so we connect 1 to 2. 2×2=4, so we connect 2 to 4, and so on.

2×100=200, where’s the 200? It goes in a circle so 200 is where the 0 is, and now you can keep going. Now you could keep going beyond 199, but actually, you’re going to get the same lines you already had!

For the code in Processing, I mapped the two numbers I wanted to connect up (call them i), which are in between 0 and 200, to a range between 0 and 2π. That gave me a fixed radius (I used 75px) and an angle (call it θ). Then I converted those to x and y by multiplying the radius by cos(θ) for x, and the radius by sin(θ) for y. That gave me a coordinate for each point (and even in between points, so you can do the in between times tables as well!) Then I connect up those coordinates with a line. Now I just do this over and over again, until all points are connected to something.

Unfortunately, Processing can only create and draw on a window that is smaller than a screen. So instead of programming a single 2000px x 4000px poster, I programmed 8 1000px x 1000px pieces. Then I just spliced them together.

Idea: Times Tables, Mandelbrot and the Heart of Mathematics video by Mathologer
Code: by Simon Tiger
Download the animated version here: https://github.com/simon-tiger/times_tables

Milestones, Physics, Uncategorized

Is the Universe random?

Simon, looking at the dust particles in the sun: “Is brownian motion random? If we look small enough, we might see something deterministic… but it might also be stochastic. What you’re doing, you might get something very little wrong, in which case you get a completely different answer! And how wrong you are in this area is being controlled by the little coins inside your head, or somewhere, which are smaller than an atom! But still, coins are deterministic. So even throwing of a coin is deterministic. It’s pseudo randomness. Looks and feels random but it’s not. If you really closely look how the coin moves then you can predict how the coin is gonna land. Technically, you can have some kind of robot to do that.

So actually, is the Universe random? It’s a very tricky puzzle”.

Me: At the quantum level, a particle can be in two places at once, but once the observer sees it, it seems to choose a specific position.

Simon: “Maybe it even depends on who is looking! Which means that we sometimes see everything wrong!.. Brownian motion is deterministic, we think”.

Murderous Maths, Uncategorized

Special Magic Square

Simon shows a very special kind of magic square in which not only the rows, the columns and the diagonals add up to the magic number but also “plus signs”, crosses, sums of diagonals – all in all, thousands of ways to make the magic number (especially if you wrap the grid around a torus). Simon also explains the equation behind the magic!

Simon learned about the equation and the way to make the square from a comment to this video on the SingingBanana channel.