# Algorithmic House, Billiards, and Picma

Welcome to this week’s Math Munch!

Check out this beautiful building:

This is the Endesa Pavilion, located in Barcelona, Spain.  It’s also called Solar House 2.0, and that’s because the tops of all of those pyramid-spikes are covered in solar panels.  But that’s not all – this house was designed to best capture sunlight in the exact location it was built using a mathematical algorithm.

To build this house, architect Rodrigo Rubio, who works for the Institute for Advanced Architecture of Catalonia, first tracked the path of the sun over the spot he wanted to build the house.  He then plugged that data into a computer program.  This program is a set of mathematical steps called an algorithm that turns data about the movement of the sun in the sky into a geometric building.  The building it creates is the best – or optimal – building for that spot.

It puts solar panels in locations on the building that get the most sunlight and orients them to get the most exposure.  It places windows of different sizes and overhangs at different angles around the house to get the best ventilation, block sunlight from entering the house, and keep the house cool in the summer and warm in the winter.   And, because it’s an algorithm, it can be used to design the optimal house for any location.  The program then creates a pattern for the wooden pieces that make up the house.  This pattern can be sent to a machine that cuts out the pieces, which builders put together like a puzzle.

In this video, Rodrigo explains how the building was designed, how the design works, and how this design can be used to make eco-friendly houses all over the world.

Next, have you ever played billiards?  Maybe you’ve played pool or watched Donald Duck play billiards.  It’s interesting to see how a pool ball moves around on a rectangular billiards table, which is how the table is usually shaped.  But it’s even more interesting to see how a ball moves around on a triangular, pentagonal, circular, or elliptical billiards table!

Want to try?  Check out this series of applets from Serendip, an exploratory math and science website started by some professors at Bryn Mawr College in Pennsylvania.  Serendip aims to help people ask and answer their own questions about the world we live in.  In these billiards applets, you can explore dynamical systems – mathematical structures in which an object moves according to a rule.   In some situations, the object will move in a predictable way.  But in other situations, the object moves chaotically.  As you play with the applets, see if you can figure out how the shape of the table effects whether the billiard ball will move chaotically or predictably.  These applets also make some beautiful star-like designs!

Finally, here’s a new game: Picma Squared.  In this game, you use logic to figure out how to color the squares in the grid to make a picture.  It starts out simple, but the higher levels are really challenging!  Enjoy!

Look for this game and others on our Games page!

Bon appetit!