From Platonic Solids to Archimedean Solids

Simon explains how to to turn Platonic Solids into Archimedean Solids, using truncation and rectification.

 

Simon explains how to convert Platonic Solids to Archimedean Solids and builds a Rhombicosidodecahedron from 62 Magformers pieces.

 

Magformers did not sponsor these videos. In fact, we’ve been sponsoring Magformers 🙂

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Tiling shapes to build dodecagon and octagon

Some outside fun: Simon uses a regular hexagon, equilateral triangles and squares to build a regular dodecagon, and right angled isoceles triangles (with sides equal to 1 and the hypotenuse equal to square root of 2), and rectangles (with sides equal to square root of 2 and 1 or square root of 2 plus 2 and square root of 2) to build a regular octagon.

Where are my compasses?

 

There’s been a lot of drawing going on here lately. And jokes, like in the video above. Yesterday, after he got distracted while trying to draw the exact tangent of a circle, Simon said: “I went off on another tangent. To find a tangent!”

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Magnitude of a 3D vector

Here Simon explains how to calculate the magnitude of a 3D vector. This is something he partially figured out on his own and partially learned from Daniel Shiffman’s tutorial on Trigonometry and Polar Coordinates.

 

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Infinite Line in Processing. Simon’s own code.

A beautiful project in Processing (Java), Simon’s own code, resembling  an El Lissitzky painting that you can control and change with the mouse (without Simon knowing El Lissitzky). Resulted from thinking about and playing with infinite line and line segments. Simon used the following formula: slope times x plus yIntercept.

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Pendulum Force

This is a beautiful “lecture” that Simon in his pajamas, chocolate paste adorning is face, game me Friday morning. He spoke about pendulum force, a force he was about to apply in a coding project.

The other videos form the very beginning of the lecture, with Simon plays with sine and cosine and explains why location, velocity and acceleration can be vectors and can be angles:

And this is the code where pendulum force is used. It’s an example from The Nature of Code book by Daniel Shiffman, from Chapter 3 on Oscillation:

Oscillation and Drag Force: Spring Project.

Today Simon was watching Daniel Shiffman’s tutorials to learn about drag force and how to apply it when building a spring simulation in p5.js. Simon wrote the formula for drag force in Microfost Word and looked up all the variables:

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While building a spring in p5.js, Simon talks about the 3 laws of Isaac Newton:

The project is based upon Daniel Shiffman’s book The Nature of Code, specifically Chapter 3 (Oscillation). Simon spent the rest of the evening studying “simple harmonic motion”, periods and amplitudes. Here is an excerpt from Daniel Shiffman’s book:

y = sine(x)
You’ll notice that the output of the sine function is a smooth curve alternating between –1 and 1. This type of a behavior is known as oscillation, a periodic movement between two points. Plucking a guitar string, swinging a pendulum, bouncing on a pogo stick—these are all examples of oscillating motion.
This is what is known as simple harmonic motion (or, to be fancier, “the periodic sinusoidal oscillation of an object”). It’s going to be a simple program to write, but before we get into the code, let’s familiarize ourselves with some of the terminology of oscillation (and waves).
Simple harmonic motion can be expressed as any location (in our case, the x location) as a function of time, with the following two elements:
  • Amplitude: The distance from the center of motion to either extreme
  • Period: The amount of time it takes for one complete cycle of motion
Looking at the graph of sine, we can see that the amplitude is 1 and the period is TWO_PI; the output of sine never rises above 1 or below -1; and every TWO_PI radians (or 360 degrees) the wave pattern repeats.