This document is a report from a 2008-2009 mathematics project group from St. Joseph's College on Pythagoras' Theorem. The report introduces Pythagoras' Theorem, provides the history of Pythagoras and Euclid, and includes examples of applying the theorem and its converse to solve for lengths in right triangles. It also discusses problems encountered in researching the topic and acknowledges sources of information.

1. St. Joseph's College 2008-2009 Mathematics Project Topic: Pythagoras Theorem Members: Ng King Hay (27) Benjamin Poon (28) Alex Tam (35) Jones Cheung (5) Alexander Shiu (32)

3. Want to know more about it

4. History of Pythagoras

5. Useful to daily life or professional

6. Know more about triangles

8. T he hypotenuse square of a right-angled triangle is equal to the square of opposite side and the adjacent side

9. a^2+b^2=c^2

12. Founding a group, the Brotherhood of Pythagoreans

13. Found the theorem and spread it out

14. Useful for us to know more about triangles

15. Examples AC^2=7^2+24^2 AC^2=625 AC=625 square Therefore AC=25

17. Know the triangle is right-angled or not

18. To know more about triangles

20. Found by a man called Euclid

21. First proposed and proved by Euclid

22. Very useful for mathematics nowadays

25. Referred to as the "Father of Geometry"

26. Wrote works on perspective and conic sections

27. Main article: Euclid's Elements

28. Examples 4^2+3^2=25 5^2=25 Because 4^2+3^2=5^2=25 Therefore this triangle is an right-angled triangle with angle X =90 degree. (converse of Pyth. Theorem)

30. Hold a meeting

31. Work as a team

32. Have arguments between members

33. Choose a suitable topic

35. Successful hold a meeting at 15 th May

36. Find some useful websites

37. Less arguments between members

39. Thank for Ms Tsoi for giving us professional ideas

40. Thank for some classmates gave us useful knowledge about Maths

41. References Books: 1. Pythagoras 's Theorem 2. Beauty proof of Mathematics 3. Converse of Pythagoras Theorem 4. Euclid Websites: 1. www.wikipedia.com 2. http://www.groups.dcs.st.and.ac.uk/ ~history/Biographies/Euclid.html 3. http://www.pbs.org/wgbh/nova/proof/ puzzle/theorem.html

42. ~End~