1.What are some components of a logical proof? How did Pythagoras connect geometric observations with mathematics? How did providing a logical proof for the Pythagorean Theorem advance ancient geometric studies?

2.Discuss and answer the following questions. What basic geometric principles did people understand before Thales? What was understood about right triangles before Thales? How did Pythagoras describe triangles? Why was the Pythagorean Theorem considered logical proof?

3.How could the Pythagorean Theorem be used in areas such as agriculture? Describe some other situations where this theorem is very practical.

4..What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain