# Greece

### Mathematician

Pythagoras is often described as the first pure mathematician. We actually don't know that much about his life or his important mathematical achievements. Even the Pythagorean theorem was known long before his time by the Chinese and Babylonians. By the way, the theorem is not named after Pythagoras directly but rather, after the religious scientific society that took his name.

Below is a visual proof of the Pythagorean theorem (to view click the image using your left mouse button and select 'play'):

But did you know the theorem can be more widely used? You do not even need squares. All you need to know that if you place 3 similar figures along the sides of a right angled triangle, that the areas of the smaller two will add up to that of the largest.

### Problem

How do you think you can prove this theorem (see image below)? Do you know how to find the area measurement of a regular pentagon? You can either measure the dimensions of the shapes and check for yourself, or perhaps try to prove it as I did above, but copying the shape and cutting the smaller shapes up so that they can fit insides the area of the bigger one.

### Interesting Fact

The Greek coastline is a very beautiful place with dozens of small islands. Many of the Greek mathematicians lived on those islands and so much of the mathematics they did had much to so with perimeter and area. In fact, the word ‘metre' means to measure around. Many Greeks were confused about the relationship between area and perimeter. Some knew that the size of the island could not be determined by how long it took to walk around the edge since many of the coastlines were quite irregular and some took longer to walk around irrespective of their area. However some landowners capitalized on the fact many Greeks did not understand the relationship and based the prices of their real estate on the perimeters rather than the areas. One story from ancient times tells of the founding of the city of Carthage. Dido was granted land the size equal to that which an ox hide could cover for her new city. She thought a bit about it and had her supporters sew strips of the ox hide together until they measured about one mile in length. Then, using the coastline as one border, the ox hide was stretched until it ended up covering about 2.5 acres of land. Clever, hey?

### Mathematician

Archimedes was born in Syracuse (287 - 212 BC). He made tremendous discoveries in mathematics that we still use to this day. He used the principles of balance to develop formulas for the surface areas and volumes of the sphere, cylinder and cone. His most famous story is about the discovery that happened while he was relaxing in a bath. The King had a crown made but was worried that it the goldsmith was going to try and cheat him out of some gold and make the crown out of a cheaper metal. He asked Archimedes if he could come up with a foolproof method for determining if the crown was indeed manufactured honestly. Archimedes discovered that the different densities of metal would displace different amounts of water and by submerging the crown; the king could see whether the crown was correctly composed. Archimedes was so excited by the discovery, he went running down the street naked exclaiming “Eureka!” [I've found it!]

In fact, Archimedes considered his most significant accomplishments were those concerning a cylinder circumscribing a sphere [see the map surrounding the earth problems], and he asked for this to be inscribed on his tomb with he died.

### Problem

Consider this. Imagine the earth was a perfect sphere and there was a cone and a cylinder that had the identical height and width. What is the relationship between their volumes? Can you make the same discovery that Archimedes did? Do you find it interesting?

### Riddle of the Sphinx

In Greek Mythology, the Sphinx was a monster with the head of a woman, body of a lion and the wings of an eagle. The Sphinx guarded the gates of the city of Thebes and would kill anyone that would not answer. She vowed that if anyone could answer her riddle, she would destroy herself. Here is her riddle.

What travels on four legs in the morning, on two legs at noon and on three legs at dusk? (type your answer using lower case letters)

Try solving the International Color Challenge!