Penrose
51 posts
@UsePenrose
create beautiful diagrams just by typing mathematical notation in plain text
Q: How do you quickly multiply multi-digit numbers? A: Draw a diagram! Just draw a line for each 10's and 1's digit of the two factors, and count the number of crossings to get the 100's (yellow), 10's (blue), and 1's (red) digits of the product! Drawn here using @UsePenrose.
The Japanese multiplication method makes everybody feel "I wish they taught math like this in school." It's not just a cute visual tool: it illuminates how and why long multiplication works. Here is the full story.
The winding number of a polygon is, quite literally, the number of times a polygon "winds" around a given point x. It can be used for inside/outside tests by just summing the angles made by each (oriented) edge: zero if x is outside, ±2π if x is inside. [Made with @UsePenrose.]
[19/n] And keep on going—how low can we go? Warning: if you make it too small, the optimization may go on forever and freeze your tab! Sorry about that. You can also slow down the optimization to a step size of 1 to see how it works:
The optimal known packing of 17 equal squares into a larger square - i.e. the arrangement which minimises the size of the large square.
