Computer Science, Crafty, Electricity, Electronics, Engineering, Logic, Milestones, motor skills, Simon teaching

Simon building an 8-bit Computer from scratch. Parts 1 & 2.

Parts 1 and 2 in Simon’s new series showing him attempting to build an 8-bit computer from scratch, using the materials from Ben Eater’s Complete 8-bit breadboard computer kit bundle.

Simon is learning this from Ben Eater’s playlist about how to build an 8-bit computer.

In Part 1, Simon builds the clock for the computer
In Part 2, Simon builds the A register (more registers to follow).
these little black things are an inverter (6 in one pack), AND gate and OR gate (4 AND and OR gates in one pack)
this schematic represents the clock of the future 8-bit computer
Simon and Neva thought the register with its LED lights resembled a birthday cake
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, Crafty, JavaScript, Simon's Own Code, Together with sis

Slitscan and Edge Detection in p5.js

Simon writes:

Made a cool #slitscan effect you all can play with: https://editor.p5js.org/simontiger/full/Xr8F_KmnU

Code here: https://editor.p5js.org/simontiger/sketches/Xr8F_KmnU

I have actually figured out the appropriate way to move the image of the webcam such that the resulting trail produces a slitscan!

Simon writes: (The second pic is also me, doing sit-ups :))
Simon’s sister playing with the slitscan effect
Simon has also created a nice edge detection effect, allowing for video images to look like they were traced in pencil
Crafty, Geometry Joys, motor skills, Murderous Maths, Simon teaching, Simon's sketch book

A Square Triangle?

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.

Almost everything he shares in this video Simon has learned from Cliff Stoll on Numberphile:
https://www.youtube.com/watch?v=n7GYYerlQWs
https://www.youtube.com/watch?v=gi-TBlh44gY

Coding, Computer Science, Crafty, Geography, Murderous Maths, Notes on everyday life, Simon's sketch book

Pathfinding algorithms: Dijkstra’s and Breadth-first search

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).

this was an example of how an algorithm can send you the wrong way if it has data of the “right” way being weighted more (due to traffic jams, for example)
Crafty, Geometry Joys, motor skills, Murderous Maths, Notes on everyday life, Simon's sketch book

A Knot Theory Puzzle

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!”

The letters x and y stand for the ways to intertwine the strings, with x wrapping around 1 and y wrapping around 3. The regular x and y are clockwise (x or y) and the inverse x and y are anticlockwise (x^-1 or y^-1). Obviously, a sequence of clockwise-anticlockwise of the same string should be avoided as it unties itself.
the moment of truth!
performing in front of our guests the day after (in Dutch)
the solution
Crafty, Geometry Joys, Group, Logic, Milestones, Murderous Maths, Notes on everyday life, Together with sis

Vladimir Krasnoukhov at MathsJam Antwerp!

all these beautiful puzzles we have received from Vladimir Krasnoukhov

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 Krasnoukhov and Simon

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 and Neva constructing the shape that “allows” to convert it into Penrose impossible triangle (as seen in the optical illusion in the Kvantik magazine)
the next step was already impossible

Simon’s also working on other math problems from the magazine, so more blog posts about Kvantik will follow. We’re very happy to have discovered the website https://kvantik.com

You can find out more about Vladimir Krasnoukhov’s puzzles on planetagolovolomok.ru

Coding, Computer Science, Crafty, Geography, Geometry Joys, Murderous Maths, Simon's sketch book

Dijkstra’s pathfinding algorithm

“I have first built a maze, then I turned it into a graph and applied Dijkstra’s pathfinding algorithm!”

a maze to which Dijkstra’s pathfinding algorithm is applied

Simon learned this from the Computerphile channel. He later also attempted to solve the same maze using another pathfinding algorithm (A-Star).

Crafty, Geometry Joys, Murderous Maths

Shaky Polyhedra

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.

Steffen’s polyhedron, a concave polyhedron, the simplest of the so-called “shaky polyhedra”
a different view of our Steffen’s polyhedron
a different view of our Steffen’s polyhedron