What a blissful day at Creative Coding Utrecht! Simon also got a chance to show a few of his projects in Processing to a cool and understanding audience!

# Category: Geometry Joys

# Physics Experiments: The Color Wheel and Mind Blending

Inspired by Physics Girl, here come a couple crafty color wheel experiments involving what Physics Girl calls “mind blending” (it may not be the real name) – mixing color wave lengths in your mind. Simon has already studied the way our brain perceives blended/ moving color before, in the several optical illusions he programmed. This time, however, he decided to observe how simple paint can produce the same effect.

CORRECTION by Simon: *You can’t actually even see the entire visible spectrum. You only see red, green and blue (I couldn’t think of that in the video)*.

The rotating green and red disk look more yellow in this extra 2 sec of footage taken by a different camera:

Simon prepared the props himself, with some help from his sister New (who painted one of the disks) and me (I helped cutting the hard cardboard). We couldn’t figure out a way to get the disks to spin fast and tried several options (like straws, pencils and even a dismantles giroscope). Eventually, we decided to use a small drill from a children’s woodworking set and it worked!

Making the fourth disk was the most difficult part as Simon wanted to divide the circle into 12 equal sectors. He came up with this elegant solution: he drew a hexagon and then bisected every angle (see below).

# Simon made his own foam Rubik’s Cube

Simon saw this design in a video by Mathologer and adapted it slightly (Mathologer used glue and no screws). He had dreamt of making a cube like this for months, but the idea of crafting one from wood seemed too complicated. Today it occurred to him that he can make the design using his new woodlike foam and press iron screws into the foam to hold the magnets! On to the wooden model now!

# Hexaflexing

Simon has been into making various hexaflexagons, inspired by the Vihart channel. It was tough at first, but later the same day he didn’t need any help anymore and flexed away:

# Optical Illusions in Leeuwarden, Friesland

Simon loved the optical illusions scattered around the town.

# Symmetric Chaos

“What you’ll find is that the path is chaotic while the points are actually symmetric,” – Simon tells me, graphing a sequence on the beach. (On the picture below, the sequence graphed is the one on the right):

# Back in Shape

Simon prepared 100 2D shapes to make over 100 solids yesterday. He started with the easy one that he had built hundreds of times before, when he was much younger (like the Platonic Solids and some of the Archimedean Solids and anti-prisms), but then went on to less familiar categories, like elongated and gyroelongated cupolae and dipyramids! Never heard of a Gyrobifastigium? Take a look below!

*Dodecahedron*

*Icosahedron*

*Cuboctahedron*

*Small Rhombicuboctahedron* (by expanding a cube)

*Icosidodecahedron*

Simon didn’t build a snub cube (“is a real challenge and has two different versions that are mirror images of each other”). Nor did he make a truncated dodecahedron (as he has no decagons), nor a truncated icosahedron (doesn’t have 20 hexagons). “If you slice the corners off of an icosahedron, you get a truncated icosahedron also known as a… football!” The 62-sided rhombicosidodecahedron he had already made many times before, we’ll post an old photo later.

And then came the antiprisms:

*A square antiprism – two squares connected with a band of equilateral triangles*

*A pentagonal antiprism*

And the elongated shapes:

*Pentagonal cupola (half a cantellated dodecahedron); there is no hexagonal cupola*

*Pentagonal rotunda (half of an icosidodecahedron)*

*Gyroelongated triangular pyramid*

*Gyroelongated square pyramid*

“If you gyroelongate a pentagonal pyramid, it looks like an icosahedron, but isn’t quite that”:

*Gyroelongated pentagonal pyramid*

*Elongated square dipyramid*

*Elongated triangular cupola*

*Gyroelongated triangular cupola*

*Gyrobifastigium* (there it is, you found it!)

*Square orthobicupola*

*Pentagonal orthobicupola* (above) *and its twisted variant – pentagonal gyrobicupola* (below), looking like a UFO

# The Paradox of the Mathematical Cone

Simon showed me an interesting paradox that’s difficult to wrap my mind around. If you slice a cone (at a random height), the section is a circle. The chopped-off part (a small cone) also has a circle as its base. Are those circles equal? They are the same, because they result from the same cross section. Hence the difference between them is 0. Now imagine slicing the cone an infinite number of times. “The difference between the circles will come up an infinite number of times: zero times infinity”, – Simon explained. “But zero times infinity has no value (or has any value, it’s indeterminate). Zero times infinity is the same as infinity minus infinity, which means that it can be whatever you want. Riemann’s rearrangement theory makes this true.”

# The game of Loop

Simon has learned about a beautiful new game from Alex Bellos on Numberphile. The game is called Loop and resembles pool. The pictures below illustrate the layout on an elliptical game board/pool table. The black hole on the left side is the pool table pocket and the black ball with number 8 on it is the black ball. The white ball is the cuball. The colored balls are the only other balls used in the game. There is a lot of Geometry in this game.

Simon has explained how the pocket and the black ball are located exactly on the focal points of the ellipse, that is why if the black ball is hit (from whatever direction) it is always going to go towards the pocket. The winning strategy in the game would thus be to hit the cuball as if it comes from a focal point.

Simon writing the rules for stages 1 and 2 of the game:

The ball always bouncing at an identical angle:

Thus always hitting the second focal point if coming from the other one:

# Rubik’s Cube Moves

Simon is getting faster and faster with the cube. Order a speed cube for his upcoming birthday? So much for “poor fine motor skills”.