Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Murderous Maths, Simon makes gamez, Simon teaching, Simon's sketch book, Together with sis

Fun crafty puzzles Simon did with Neva

Three boxes with fruit, all the three labels are misplaced. What is the minimum number of times one will have to sample a random piece of fruit from one of the boxes to know how to label all the three boxes correctly? From Mind Your Decisions.

Connect A and A’, B and B’, C and C’, D and D’ so that no lines intersect. (Neva added colors).

Dividing 11 coins among three people: “How many ways can you divide 11 coins to 3 people? How many ways are there if each person has to get at least 1 coin?” From Mind Your Decisions.

Solving a simple quadratic equation geometrically: the geometric interpretation of “completing the square”, a notion from deriving the quadratic formula. From Mind Your Decisions.

Which way do the arrows point? (Simon made this drawing in Microsoft Paint):

Coding, Community Projects, Contributing, Geometry Joys, Group, live stream, Milestones, Murderous Maths, Notes on everyday life, Physics, Python, Simon's Own Code

Live Session with Stephen Wolfram and the Wolfram Demo Project, World Science Scholars.

Simon has completed the course A New Kind of Science with Stephen Wolfram and the World Science Scholars program. Which doesn’t mean he is done with digging deep into Wolfram’s groundbreaking new kind of science! (As a matter of fact, he is still reading Wolfram’s 1500-page book. And as Professor Wolfram told Simon during the live session, there’s nothing in the book that no longer holds).

Simon happy after a major break-through in his demo project, hoping to present his findings to Stephen Wolfram the same evening

At the live session, a few scholars including Simon were planning to present their Wolfram Language demos, but Professor Wolfram was so inspired by his current research that he decided to share his latest discoveries instead (he is tiptoeing closer to laying the foundations of a theory that would unify all natural sciences based on his principle of computational equivalence). It was a very engaging session (even though Simon’s video camera malfunctioned, which hardly mattered).

screenshot of the live session
Danielle Rommel, who works with Professor Wolfram, told Simon she had actually been watching videos on his YouTube channel!

As for Simon’s demo project, that’s a whole story. It took Simon weeks to define what he was actually going to pick as his topic and once he had picked his topic, he didn’t know where to start (because he managed to pick an NP problem). He suggested to collaborate together with another World Science Scholar, as it was that boy who initially inspired to think in the direction of the particular open math problem. The two of them had two long video chats. (It was so much fun to observe them, they both had zero interest in small talk and went straight down to the math, without even saying hi).

Simon during a video chat with a fellow student, discussing the project
ways to write graph data that Simon shared with his fellow student during their talk

Unfortunately, after the original project presentation during the live session with Stephen Wolfram was cancelled, Simon’s partner never really replied to Simon’s chat messages (until weeks later). Simon did manage to get part of the demo done (porting a huge graph into the Wolfram Language, which required writing separate code in Python), but felt stuck later, after several attempts to color the graph failed. He ended up spending several days writing several more Python scripts. We have documented the process on video. The project has turned into a computational essay and it’s definitely still unfinished, but I’m not sure Simon will come back to it in the near future. He got a couple of minutes to present his findings at another live session last week (with a World Science Scholars teaching fellow Aaron Mertz and Rory Foulger, Education Outreach Coordinator at Wolfram Research), but was confused as he didn’t get any feedback about his findings and got the impression his main questions weren’t understood. He was also a bit annoyed with me yelling on the background about what he should do and say (I saw he was confused and was afraid his time would be cut short, so I wanted to make sure he would mention his main points). I’ve learned my lesson now and have decided not to interfere with his live performances anymore, not to put him under additional pressure.

Simon has also written to Professor Wolfram, currently awaiting his reply. His main questions were:

I was surprised to discover that no Heule or de Grey graphs exist (anymore?) built into the Wolfram Language. As part of my research, I’ve created a very long list of all the graphs the Wolfram Language knows about, and HeuleGraph is not in the list. I tried to pose this question during the short discussion of my project at the World Science Scholars live session this week, but didn’t get any feedback (I don’t think my question was understood). Yes, one is able to find images of Heule graphs in Wolfram notebooks, (like this one https://notebookarchive.org/heule-graph–2019-07-0z3zu9k/) and on Wolfram MathWorld (like here http://mathworld.wolfram.com/HeuleGraphs.html). But those are just pictures in archived notebooks, and even if I try to copy/paste the code into my own notebook, it doesn’t work.

My second question concerns coloring such a large graph in the Wolfram Language: do you think it could be possible? As I don’t know a built-in function to do that within the Wolfram Language (and I don’t think such a thing exists), I decided to try to color the graph in Python and then upload it into my Wolfram notebook. I created another Python script to make the graph easier to color, and yet another Python script to actually color all the vertices (using Breadth-First Search). The problem was: it didn’t color it with only 5 colors (but with 8)! I made a video about the making of the project, with me explaining why this task is hard for a computer to do, and even some computational complexity theory!

Timecodes: Converting to CSV: 0:00 Generating the Colors: 23:06 Some Math: 42:16 Part I Conclusion: 56:46

this video is long, but even briefly scanning through its several parts gives a thorough impression of Simon’s current math and coding abilities

The project is attempting to visualize the Hadwiger–Nelson problem from geometric graph theory: what is the minimum number of colors required to color the plane (chromatic number of the plane) such that no two points at distance 1 from each other have the same color. It’s an unsolved problem, but we know that the answer is 5, 6 or 7. In 2018, Aubrey de Grey proved that the chromatic number of the plane is at least 5. His smallest unit-distance graph with chromatic number 5 had 1581 vertices. Several smaller graphs have been found since then, a major contribution done by Marijn Heule, who has come up with his own method of reducing the size of graphs. In 2019, Heule constructed the smallest unit-distance graph with chromatic number 5 so far, with 517 vertices. (Side-note: since I decided I’m going to use the 517 graph, I have actually found a smaller Heule graph with 508 vertices, but it was of a data format that I wasn’t able to use anyway). The goal of my project was to color such a graph in Wolfram language, to create a Wolfram Demo.

In Part 2, I tried to code yet another Python script to group the graph into smaller units to make a smaller graph, and color that one, then blow each vertex back into the unit considered.

Link to Simon’s Wolfram Notebook: https://www.wolframcloud.com/obj/9795e37e-aa73-4ae6-8249-81223ffdbc7f Link to my code on GitHub: https://github.com/simon-tiger/Hadwiger-Nelson-Project-Data

Simon reading Marijn Heule’s paper “Computing Small Unit-Distance Graphs with Chromatic Number 5”

Link to Marijn Heule’s paper “Computing Small Unit-Distance Graphs with Chromatic Number 5”: https://arxiv.org/pdf/1805.12181.pdf

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: https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html

Interactive full-screen version, allowing you to change the seed and the grid size: https://editor.p5js.org/simontiger/full/2CrT12N4

Code: https://editor.p5js.org/simontiger/sketches/2CrT12N4

Screen shot of The Coding Train website with a link to Simon’s contribution
Contributing, Geometry Joys, Group, Math and Computer Science Everywhere, Math Riddles, Milestones, Murderous Maths

Simon solving Brilliant’s daily challenges

Simon keeps thoroughly enjoying Brilliant’s approach to intelligence and learning (even though he sometimes dislikes the way the daily challenges are formulated). His latest stats:

From the courses he has done most I conclude he’s mostly into Computer Science and real world problem solving at the moment:

Below are some screen shots of the daily challenges he was especially curious about lately and also excerpts of his taking part in Brilliant’s discussions:

Simon contributing to the discussion of the January 2 challenge
January 13 challenge

I noticed it’s a cyclic quadrilateral and I know that the opposite angles of a cyclic quadrilateral have to add up to 180 degrees. At first I thought: How am I even going to go about doing it, because it’s so cryptic and so full of information. But once I solved it, it actually became quite easy to draw!

February 4 challenge
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