## The fractal and geometric beauty of plants Jul 12 2016

When you look at some plants, you can just see the mathematics behind how the leaves, petals, and veins are organized.

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)

Unknown fractal. It's sort of like a Sierpinski gasket but with circles. (via migurski)

**Update:** Turns out that this fractal is "the orbit of a circle under a Kleinian group generated by two Mobius transformations". (thx, david)

Using a geometric shape called a Reuleaux triangle, it's possible to drill square holes. Click through for all the exciting math!

**Update:** A video of a Reuleaux triangle rotating in a square. (thx, will)

**Update:** More on the Reuleaux triangle at MathWorld. (thx, nevan)

**Update:** The Reuleaux triangle is also the basis for the Wankel engine.. (thx, brian & adam)

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