# Natural Geometry, Hex, and Sacred Geometry

Welcome to this week’s Math Munch!

People can be skeptical when some mathematicians and scientists talk about mathematics as the “mysterious code” that “underpins the world.” I mean, the natural world is so chaotic! But then you run across this:

Honeycombs are remarkably symmetrical. Each little cell is a perfect hexagon – and all bees build this way. Why? Because of mathematics.

NPR’s Robert Krulwich wrote about this in a recent post on his excellent science blog, Krulwich Wonders. I think the explanation is an amazing example of how the natural world often follows mathematical rules perfectly. Thousands of years ago, an ancient Roman scholar named Marcus Terrentius Varro conjectured that the hexagon is the shape that most efficiently breaks flat space up into little units – making honeycombs that hold the most amount of honey while using the least amount of wax. He couldn’t prove his idea, though. It remained a conjecture until 1999 when a mathematician named Thomas Hales finally proved it! You can read a summary of his proof here. Or, watch this snippet about bees and their hexagonal honeycombs from the BBC.

Want to learn more about hexagons? Here’s a website devoted entirely to the geometry of hexagons!

Speaking of hexagons, have you ever played the game Hex? It’s a two-player game in which players take turns claiming hexagons on a hexagonally-tiled board, trying to create a connected path from one end of the board to the other. You can play it by hand using a sheet of hexagon graph paper, or you can play against a computer online, here. Enjoy!

This stained-glass church window is an example of sacred geometry.

Bees aren’t the only animals who use symmetry in the things they make. Humans do, too – especially for spiritual purposes.

An Islamic tiling.

Humans have been in awe of the symmetrical laws that seem to govern the universe for thousands of years, and they’ve developed a type of artwork called  Sacred Geometry, a way of thinking that gives spiritual significance to geometric shapes. Sacred geometry can be found in religious artwork from many different cultures, and often uses tilings of regular polygons, the Platonic solids, and interlocking circles arranged in symmetric patterns.

Mathematical artist Mark Golding has been making modern works of sacred geometry art of his own. His works are inspired by mandalas, Hindu and Buddhist spiritual symbols that represent the symmetry in the universe. The image to the right is called, “Inner Relationships.” It shows an octahedron, one of the Platonic solids, nested inside of a snub cube, which is made by chopping off the corners of a cube. I love how it demonstrates the symmetric relationships between these two shapes. If you’d like to see more of his work, check out this online gallery.

Bon appetit!

P.S. – You may have noticed a new link off to the right at the top of the page. The Math Munch Team is proud to announce that our TEDx NYED talk has been posted online!

We’re honored to have been invited to participate in this event with many other creative and accomplished educators – and we encourage you to watch the other talks from the day, too.

P.P.S. And if you’re in the mood for some more TED-style math inspiration, you might enjoy these miniTED talks about math by some of Justin’s seventh graders.