This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
Simon explains what Gaussian formula is to check a shape’s curvature and shows how to make a triangle with three 90° angles. Or is it a square, since it’s a shape with all sides equal and all angles at 90°? He also says a few words about the curvature of the Universe we live in.
The photos below show Simon playing with Breadth-first search and Dijkstra’s algorithms to find the most efficient path from S to E on a set of graphs. The two more complex graphs are weighed and undirected. To make it more fun, I suggest we pretend we travel from, say, Stockholm to Eindhoven and name all the intermediate stops as well, depending on their first letters. And the weights become ticket prices. Just to make it clear, it was I who needed to add this fun bit with the pretend play, Simon was perfectly happy with the abstract graphs (although he did enjoy my company doing this and my cranking up a joke every now and then regarding taking a detour to Eindhoven via South Africa).
Simon has shown us a curious puzzle: if you hang a poster on a string using two pins, what is the way to arrange the string so that the poster definitely falls once you remove any pin? The math behind the trick involves Knot Theory. Simon has learned the trick from this video by Jade, the creator of the science and phlosophy Up an Atom channel that Simon loves.
It’s relatively easy to solve the puzzle for one particular pin. The picture below shows the solution for removing the right pin:
But the puzzle asks us to think of a configuration that makes the poster fall once ANY pin is removed, doesn’t matter which! And that’s way more difficult. Simon said that we should simplify the problem by removing the poster altogether and replacing the pins with two small loops of string.
What Simon did next was show us the math behind the trick, trying to come up with such a combination of the three loops that would stay connected but, if you remove any of the three, the rest of the construction would fall apart. “Wait, that sound familiar! We’ve actually turned the problem into Borromean rings!”
When we arrived at the MathsJam last Tuesday, we heard a couple of people speak Russian. One of them turned out to be a well known Russian puzzle inventor Vladimir Krasnoukhov, who presented us with one colorful puzzle after another, seemingly producing them out of thin air. What a feast! Simon got extremely excited about several puzzles, especially one elegant three-piece figure (that turned out to have no possible solution, and that’s what Simon found particularly appealing) and a cube that required graph theory to solve it (Simon has tried solving the latter in Wolfram Mathematica after we got home, but hasn’t succeeded so far).
Vladimir told us he had been making puzzles for over 30 years and had more than 4 thousand puzzles at home. Humble and electricized with childlike enthusiasm, he explained every puzzle he gave to Simon, but without imposing questions or overbearing instructions. He didn’t even want a thank-you for all his generosity!
Vladimir also gave us two issues of the Russian kids science magazine Kvantik, with his articles published in them. One of the articles was an April fools joke about trying to construct a Penrose impossible triangle and asked to spot the step where the mistake was hidden:
Simon was very enthusiastic about trying to actually physically follow the steps, even though he realized it would get impossible at some point:
Simon has been studying various polyhedra and programming them in Wolfram Mathematica. He asked me to help him build one of the many “shaky polyhedra” from paper. The main characteristic of these polyhedra is that they always remain flexible, even if their faces are made of superrigid material. We have made the simplest shaky polyhedron, called Steffen’s polyhedron. If a shaky polytope is 3D or higher, it’s always concave.