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:
In the video below, Simon is showing the cloud design he contributed to the community project collecting cloud designs for the Processing Community Day coming up on October 21, 2017. You can play with Simon’s design on the community project webpage created by Coding Train at https://codingtrain.github.io/CommunityClouds/
Simon’s cloud is called “Round Cloud”. Once you open it on the Coding Train Community Clouds page, the cloud changes its shape every time you click on it.
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!”
Oops, the Magformers are back in our life. I thought that Simon was over Magformers (which he built with excessively when he was six), but he has picked them up again and taken them to a new level. He seems to be using Magformers to illustrate his increasingly philosophical thoughts in the pauses he takes between lessons and programming. Yesterday, he was quite disturbed after building with the mirror piece for a while and said: “What if two mirrors reflect each other? Would that stop time?” He added: “Just for safety, I’m going to put the mirror in the box. Never, never ever put two mirrors opposite to each other!”
He hasn’t made it interactive yet though. This was the original plan but he got stuck.
Here is the link: https://thimbleprojects.org/simontiger/315031/
(it’s on this new thimble.mozilla.org online code editor)
What specially delights me about Simon’s works lately is the subtle sense of humour he writes with (probably acquired through both watching Daniel Shiffman’s videos and reading Murderous Math books):
The project isn’t finished yet as the example Simon is linking to the website is only for an ellipse and a superellipse yet:
Simon also plans to add other shapes to the website later.
We’re back from a beautiful vacation in France and Spain, and it’s official now: All Shapes and Sizes by Murderous Maths’ Kjartan Poskitt is the winner!
And the runner up:
“Optical Illusions” by Russian mathematician Jacob Perelman.
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 has been studying various 2D collisions (via the p5.collide2D library and paulbourke.net), especially the Circle-Rectangle Intersection (Collision). He was so busy with this problem that he even put it down in chalk at the playground:
And on the whiteboard at home:
And spent nearly his entire math lesson today talking about the math behind 2D object collision to his math teacher:
Simon also used Circle-Rectangle Collision for his awesome new Hero Game in Processing!
Simon playing around with sine, cosine and radii in Grapher: