Crafty, Electricity, Electronics, Engineering, Experiments, Geometry Joys, Notes on everyday life, Physics, Simon teaching, Together with sis

Vanishing Letters

Simon’s way to celebrate Helloween: a little demo about how red marker reflects red LED light and becomes invisible. A nice trick in the dark!

We also had so much fun with the blue LED lamp a couple days ago when Simon discovered that it projects perfect conic sections on the wall! Depending on the angle at which he was holding the lamp, he got a circle, an ellipse, a hyperbola and a parabola! Originally just a spheric light source we grabbed after the power went out in the bathroom, in Simon’s hands the lamp has become an inspiring science demo tool.

Experiments, Geometry Joys, Murderous Maths, Notes on everyday life, Physics, Together with sis

The Puzzle Man is Back!

Guess who was in town in mid-October? The amazing Vladimir Krasnoukhov, a one-of-kind puzzles inventor from Russia! (I know, I should’ve written about this earlier, but I’ve been lagging behind with my blog posts because of a really wicked bronchitis). He stopped by for a coffee and literally showered Simon with new mind boggling gifts!

Simon was especially impressed by the two physics demos that look like stuffed surfboards (Vladimir calls them “oysters”) and can only rotate in one direction due to the moment of inertia. Vladimir told us there have even been research papers written about these demos! Simon has been showing the trick to just about everyone who has visited our home ever since.

We have also received an especially difficult puzzle that took famous Russian physicist Sergei Kapitsa two hours to solve (Vladimir told me the answer, he didn’t want me to waste two months of my life) and several more colourful and elegant models. Simon is not even particularly keen on puzzles (when it comes to recreational maths, I think he is more into riddles and proves), it is Vladimir’s friendly disposition, his selfless devotion to mathematical beauty and his deep respect for a child’s intrinsic interests, his deep respect for children’s play in general, that have made our hearts melt. You can find out more about Vladimir Krasnoukhov’s puzzles on planetagolovolomok.ru

Simon rotating the “oyster”
Geometry Joys, Group, Math Riddles, Murderous Maths, Museum Time, Notes on everyday life, Together with sis, Trips

Mind Mystery

Our visit to Mind Mystery, a place featuring a few famous optical illusions and math puzzles museum in the Dutch province of Limburg was really impressive.

by the entrance
this was my favourite effect, it felt like we were trapped in the Interstellar Tesseract (amazing how beautiful sphere can be shaped by a little mirrored tunnel with an LCD screen on the back wall, the trick is that the tunnel was not rectangular but trapezium-shaped, Simon explained)
and then Simon’s sister Neva lost touch with gravity
the only way to deal with that was to flip the whole building! and look there, at the back of the courtyard, isn’t that Penrose’s impossible triangel made possible?
if you look through the peephole, the triangle’s vertices seem to be touching
ahm… an Euler torus?
and we have finally tried a mirror maze
Simon playing with the Towers of Hanoi, applying a new algorithm; when we got home, Simon actually wrote a Python program that spits out the solution for up to 9 disks!
Upon coming home, Simon tried recreating one of the tricks he encountered at the museum, the 63-digit-number trick, and has discovered that the trick doesn’t always work!
no matter how exciting Mind Mystery was, this slide was ranked as the top activity by the kids, together with a similar slide in the neighbouring swimming pool (in the
Geometry Joys, Math and Computer Science Everywhere, Math Tricks, Murderous Maths, Notes on everyday life, Simon teaching, Simon's sketch book

Sums of consecutive numbers

While waiting to pick his little sister up from a ballet class, Simon explaining general algebraic formulas to calculate the sums of consecutive numbers. He derives the formulas from drawing the numbers as dots forming certain geometric chapes.
consecutive integers
consecutive odd integers
Crafty, Geometry Joys, Good Reads, Logic, Murderous Maths, Simon teaching, Simon's sketch book

Attractiveness vs. Personality

Debunking the stereotype that all attractive guys/girls are mean, something Simon has learned from MajorPrep and the How Not to Be Wrong book by Jordan Ellenberg. The slope in dark blue pen shows our scope of attention, a pretty narrow part of the actually diverse field of choices.
art, Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Murderous Maths, Notes on everyday life, Simon makes gamez, Simon teaching, Simon's sketch book, Together with sis

Math puzzles: Is it Possible?

Simon has been fascinated by these possible-impossible puzzles (that he picked up from the MajorPrep channel) for a couple of days. He prepared many paper visuals so that Dad and I could try solving them. This morning he produced this beautiful piece of design:

Simon showing one of the puzzles to another parent while waiting for Neva during her hockey training
Simon’s original drawing of the doors puzzle. The solution of the puzzle is based on graph theory and the Eulerian trail rule that the number of nodes with an odd degree should be either 0 or 2 to be able to draw a shape without lifting your pencil. The number of rooms with an odd number of doors in the puzzle is 4 (including the space surrounding the rectangle), that’s why it’s impossible to close all the doors by walking though each of them only once.
Simon explaining odd degree nodes
Computer Science, Electronics, Geometry Joys, Logic, Math and Computer Science Everywhere, Murderous Maths, Notes on everyday life, Simon's sketch book, Trips

Doing math and computer science everywhere

One more blog post with impressions from our vacation at the Cote d’Azur in France. Don’t even think of bringing Simon to the beach or the swimming pool without a sketchbook to do some math or computer science!

This is something Simon experimented with extensively last time we were in France. Also called the block-stacking or the book-stacking problem.
Simon wrote this from memory to teach another boy at the pool about ASCII binary. The boy actually seemed to find it interesting. A couple days later two older boys approached him at the local beach and told him that they knew who he was, that he was Simon who only talked about math. Then the boys ran away and Simon ran after them saying “Sorry!” We have explained to him that he doesn’t have to say sorry for loving math and for being the way he is.
Drinking a cocktail at the beach always comes with a little lecture. This time, the truth tables.
Coding, Contributing, Geometry Joys, Math Tricks, Murderous Maths, Python, Simon teaching, Simon's Own Code, Simon's sketch book

Why the Golden Ratio and not -1/the Golden Ratio?

Take any real number and call it x. Then plug it into the equation f(x) = 1 + 1/x and keep doing it many times in a row, plugging the result back into the equation.

At some point you will see that you arrive at a value that will become stable and not change anymore. And that value will be… φ, the golden ratio!

But this equation also has another answer, -1/φ. If you plug that value into the equation, it will be the same, too. The real magic happens once you have rounded the -1/φ down (or up), i.e. once what you plug into the equation is no longer exactly -1/φ. What happens is that, if you keep going, you will eventually reach… φ as your answer!

Simon saw this interesting fact in a video by 3Blue1Brown and then came up with a proof as to why it happens.

Simon also sketched his proof in GeoGebra: https://www.geogebra.org/classic/zxmqdspb

Crafty, Geometry Joys, Math Tricks, Murderous Maths, Simon teaching, Simon's sketch book

Inscribed angle theorem

“It reveals itself once you complete the rectangle to find the centre. Because, of course, the diagonal passes through the centre once you inscribe a rectangle inside the circle, because of the symmetry”.
Tiling the quadrilaterals Simon has crafted applying the inscribed angle theorem.
Tiling the “shapes generated by the inscribed angle theorem”
“The theorem says that if you have a circle and just three random points on it, then you draw a path between te first point to the second, to the centre, to the third point and back to the first point”.
art, Coding, Geometry Joys, Murderous Maths, Museum Time, Notes on everyday life, Together with sis, Trips

Back at Stedelijk

As for Morellet’s RGB colored cells, very inspiring for a sandpiles coding project. (The photographs don’t convey half of the effect the original canvasses invoke. Morellet’s cells actually appear to be moving when you gaze at the original).
Installation by Barbara Kruger
Installation by Barbara Kruger
Read this poem from top to bottom and it’s depressing, from bottom to top and it’s empowering.