Simon and Neva make a 3D projection of a Hypertetrahedron – one of the regular solids in 4D – using straws. Simon looks up the formula for the center of the tetrahedron (radius of its circumscribed sphere) to measure the sides of the inside straws. To cut the exact length of the inside straws, he constructs a segment with the length of square root of six, divides it by 4 and multiplies the result by the original length of the straws.
Please also see our next and even cooler project – a 3D projection of a Hyperoctahedron:
The Hyperoctahedron came out to look very nice and four-dimensional. “It lands on the floor very nicely”, Simon says throwing it around – it is a very stable shape, made up of 16 tetrahedrons. Simon had to work out the centre of the triangle for this projection, which is easy to do for equilateral triangles.
The making of the Hyperoctahedron:
Measuring the center of the equilateral triangle:
Cutting the straws so that their length equals the distance between the vertex and the centre of the triangle:
The Hyperoctahedron is ready:
“I’m holding a four-dimensional shape in my hands!”
This is a Japanese version of the famous River Crossings Puzzle that Simon learned from the Scam School channel (yes, our little programming and math nerd actually watches Scam School, a channel dedicated to social engineering at the bar and in the street!)
The answer, a sequence of 17 moves:
Simon showing the classic River Crossings puzzle to friends
Math graphs for solving the simple and the more advanced River Crossings puzzles using minimum vertex covers and Alcuin Numbers (learned via Numberphile):
And Simon learned that a Mobius ring is a knot, too.
Just look at those precious mathematical jewels!
And just think of all the tricks you can come up with!
Simon’s favourite trick, something he learned from Matt Parker, is quickly calculating the sum of all the faces he can’t see (the faces of the dice that stack on top of one another):
The thing is that two opposite faces on every die always sum up to the number of faces plus one (21 in the case below, as an icosahedron has 20 faces):
And 13 on the next picture, because a dodecahedron has 12 faces. To say the sum of the faces you can’t see you simply calculate n (number of faces) + 1 and multiply that by the number of dice, minus the top face.
Simon has crafted a nice game today, inspired by a video in which mathematician Katie Steckles shows several mathematical games. Simon wasn’t sure what the game was called so he named it “Reds and Greens”. The objective of the game is to accumulate a set of three cards sharing the same property (such as the same number of green dots or red dots, the same total number of reds and greens or a set in which all the three possible variants – one, two and three dots of the same color – would be present). Each player pulls a card from the stack (all the cards are lying face up) and the one who collects a set first wins. Simon has actually programmed the cards in Processing (Java) – quite a strenuous task. Below is the jpeg pic of what he made and his code in Processing.
Simon also explained how the game is very similar to Tic Tac Toe, look at the photo below and you’ll see why:
Today is one of the most beautiful days in Simon’s life: NYU Associate Professor and the creator of Coding Train Daniel Shiffman has been Simon’s guarding angel, role model and source of all the knowledge Simon has accumulated so far (in programming, math, community ethics and English), and today Simon got to meet him for the first time in real life!
Daniel Shiffman posted:
In this video, Simon explains the math behind predictions in Penny’s Game and draws a predictions diagram. Inspired by a Numberphile video.
Looking at the Moon and the Orion nebula from a roof top together with a true friend
The telescopes were brought to the panorama floor of the museum “het MAS” by the Urania observatory staff and volunteers, including Robert Matheus – a very special someone who has already done so much for us in the past.
Simon into Simon’s eyes, is it like a mirror reflected by a mirror? (Simon’s best friend is also called Simon).
Simon’s classical repertoire has extended to include some jazz, although he still seems to prefer Brahms and Bach. And the math of music.