Simon pulled out his old Magformers Pythagoras set and this time around, he really nailed all the tasks independently. The set offers a variety of puzzles to “prove” the Pythagorean theorem and apply it to other shapes (even 3D!), as well as teaches several more tricks (such as the ratios between the areas of similar triangles or the areas of parallelograms).
Chinese square Proof:
Area of Parallelograms:
Applying Pythagorean theorem to other shapes:
Extended theorem by the Greek mathematician Pappus:
Areas of Similar Triangles:
More of Pythagorean theorem with various shapes:
Simon built this #recursion example/ pattern (a Sierpinski triangle) in Codea (using the language Lua) while we a had a coffee at a cafe:
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!”
Simon is talking about various shapes having various number of dimensions, which, oddly enough, doesn’t have to be a whole number. Based on maths tutorials on 3Blue1Brown channel, that Simon has been watching a lot over the past several days.
Simon built a program in Codea visualizing the absolute value of a vector:
A set of awesome Codea tutorials that Simon recorded for those who are just starting to program in Codea. Simon ported examples from Processing (java) into Codea (Lua):
In the second tutorial (in two parts), Simon explains how to write a physics simulation program in Codea using forces like gravity, friction and spring force. Anyone watching will get to use some trigonometry and see what arc-tangent is for! The original code in Java comes from Keith Peters (Processing).
Here are some notes from when Simon was explaining the arc-tangent to me the other day:
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.
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.
Some more translations, this time from Codea (Lua) into Processing (Java).
Physics Lab tests from Codea: