Crafty, Geometry Joys, Math and Computer Science Everywhere, Murderous Maths, Simon teaching, Together with sis

Spherical Geometry

After Simon read up on spherical geometry on, he and Neva crafted some pretty colorful half-spheres. How’s that as an alternative to Easter eggs?

They also had fun looking for shortest routes across the Atlantic applying their knowledge of geodesics.

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, Coding Everywhere, Experiments, JavaScript, Milestones, Murderous Maths, Simon teaching, Simon's Own Code, Simon's sketch book

How Many Dice Rolls Until You Get a Repeat. A Probability Experiment in p5.js

How many times, on average, do you have to roll a dice until you get a repeated value? I saw this probability challenge on the Mind Your Decisions channel. I decided to test it experimentally. First, I repeated the experiment myself in two sets of 50. Then I created a diagram in the Wolfram Language to visualize the distribution. Finally, I made a p5.js sketch to roll the dice thousands of times.

repeated the experiment in two sets of 50

Link to my code:

Link to my Wolfram Notebook:

explaining the math to dad at dinner

The math behind this project come from this Mind Your Decisions challenge video and this Mind Your Decisions solution video.

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:

Interactive full-screen version, allowing you to change the seed and the grid size:


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
Geometry Joys, Murderous Maths, Simon teaching

Hyperbolic space

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.