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## Short Essay Questions Key

**1. Describe what the Egyptians knew about geometry and triangles before Hippocrates.**

The early Egyptians knew some of the properties of specific shapes such as right triangles with sides of 3, 4, and 5 units but did not develop the higher theories that examine these relationships.

**2. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?**

Pythagoras proved what is now called the Pythagorean Theorem, which holds that for any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs (a2+b2=c2). With Pythagoras, the concept of providing a logical proof for observed geometric properties fully matured.

**3. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?**

Hippocrates was a teacher from the island of Chios. He was perhaps the first to take the idea of constructing a geometry from basic elements by proving subsequently more complex theorems based on earlier proofs. However, nothing remains of his proofs. They are only known through reference from later mathematicians.

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