In a perfect world, if you place a cue ball at the focal point of an elliptical pool table, you can hit it in any direction you want and it will go into a pocket located at the other focal point. Geometry! Of course, in the real world, you need to worry about things like hitting it too hard, variations in the table, spin on the ball, etc., but it still works pretty well.
How would you play an actual game on an elliptical table though? Like this. (Hint: to sink the intended ball on the table, hit it as though it came from the opposite focal point.)
When you look at some plants, you can just see the mathematics behind how the leaves, petals, and veins are organized.
With hindsight, it seems bloody obvious the Sun and not the Earth is the center of the solar system. Occam’s razor and all that. (via @somniumprojec)
Planet Money: always buy the bigger pizza because geometry.
The math of why bigger pizzas are such a good deal is simple. A pizza is a circle, and the area of a circle increases with the square of the radius.
So, for example, a 16-inch pizza is actually four times as big as an 8-inch pizza.
And when you look at thousands of pizza prices from around the U.S., you see that you almost always get a much, much better deal when you buy a bigger pizza.
More than you’ve ever wanted to know about the Sierpinski triangle.
Throughout my years playing around with fractals, the Sierpinski triangle has been a consistent staple. The triangle is named after Wacław Sierpiński and as fractals are wont the pattern appears in many places, so there are many different ways of constructing the triangle on a computer.
All of the methods are fundamentally iterative. The most obvious method is probably the triangle-in-triangle approach. We start with one triangle, and at every step we replace each triangle with 3 subtriangles:
The discussion even veers into cows at some point…but zero mentions of the Menger sponge though? (via hacker news)