Pythagoras+and+Euclid


 * Pythagoras and Euclid**


 * My report is on Pythagoras and Euclid. Both of these people have influenced the world in the fields of science and mathematics in several ways. Pythagoras started an entire civilization. Euclid created geometry, which has been used greatly for hundreds of years. Both of these are great accomplishments that have changed history in a positive way.**
 * Throughout this report, I will expand on the accomplishments and lives of both of these mathematicians. These were both very important historical figures that have made an impact on the every day world.**


 * Pythagoras and Euclid**
 * I.** **Euclid**
 * A.** **One of Euclid's accomplishments was his 13 volume book The Elements**
 * 1.** **This book is known as the base of geometry**
 * 2.** **This book created geometry and led to the very structure of technology and building**
 * a.** **Without geometry it would be very hard to build things.**
 * b.** **geometry allows us to make measurements that are essential in manufacturing and producing**
 * B.** **Euclid** **was known for being a historical mathematician**
 * 1.** **Euclid** **created geometry**
 * 2.** **His book included all of the fundamentals in geometry**
 * a.** **Volumes 1-6: Plane Geometry**
 * b.** **Volumes 7-9: Number Theory**
 * c.** **Volume 10: Eudoxus' Theory of Irrational Numbers**
 * d.** **Volumes 11-13: Solid Geometry**
 * C.** **Euclid** **had many jobs**
 * 1.** **Mathematician**
 * 2.** **Teacher**
 * 3.** **Inventor**
 * II.** **Pythagoras**
 * A.** **At about the age of 30, he moved to a Greek colony in southern Italy.**
 * 1.** **There he founded a secret society known as the Pythagoreans.**


 * B.** **Many important concepts of mathematics and science have been credited to the Pythagoreans.**
 * 1.** **They proved that certain measures, such as the diagonal of a square, cannot be expressed as a ratio of two whole numbers.**
 * a.** **This discovery was difficult for them to accept because it contradicted their own philosophy**
 * b.** **For a time they tried to keep it secret.**
 * c.** **Such numbers were later classified as irrational numbers.**
 * 2.** **It is also thought that the Pythagoreans recognized that Earth is a sphere, that Venus is both the morning and the evening star, and that the planets are at different distances from Earth.**
 * C.** **The Pythagorean Theorem**
 * 1.** **It was known to ancient civilizations,**
 * a.** **Though he may have demonstrated its first proof.**
 * 2.** **The theorem states that in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.**


 * Pythagoras**


 * Pythagoras was a mathematician that benefited people in many ways. When Pythagoras was 30 he founded a secret society. This society was the Pythagoreans. The Pythagoreans were a Greek colony. The colony was located in southern Italy. The Pythagoreans are credited for many important concepts of science and mathematics. They proved that certain measures, such as the diagonal of a square, cannot be expressed as a ratio of two whole numbers. This discovery was difficult for them to accept because it contradicted their own philosophy. For a time they tried to keep this discovery a secret. Such numbers were later classified as irrational numbers. It is also thought that the Pythagoreans recognized the earth is a sphere, that Venus is both the morning and the evening star, and that the planets are at different distances from the earth. The Pythagoreans created a theorem known as the Pythagorean Theorem. It was known to other civilizations, though Pythagoras may have demonstrated its first proof. “The theorem states that in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.”***


 * Euclid**
 * Euclid was known for being a historical mathematician. He made many great accomplishments. One of Euclid’s accomplishments was his 13 volume book __The Elements__. This book is known as the base of geometry. This book created geometry and led to the very structure of building and technology. Without geometry it would be very hard to build things. Geometry allows us to make measurements that are essential in manufacturing and producing. His book included all the fundamentals in geometry. His book is as follows: Volumes 1-6: Plane Geometry, Volumes 7-9: Number Theory, Volume 10: Eudoxus’ Theory of Irrational Numbers, and Volumes 11-13” Solid Geometry. Euclid also withheld many jobs. Not only was he a mathematician but a teacher and inventor as well.**


 * Taken from “Euclid’s Life” @ http://derrel.net/math/euclid/euclid_life.htm**


 * Need to Know**
 * 1) **Pythagoras founded the Pythagoreans.**
 * 2) **Pythagoras worked with the Pythagoreans and created the Pythagorean Theorem.**
 * 3) **Pythagoras was a scientist and mathematician.**
 * 4) **Euclid wrote a 13 volume book __The Elements__**
 * 5) **Euclid** **created geometry.**
 * 6) **Euclid was a mathematician, inventor, and a teacher.**


 * Resources**
 * Web**
 * 1. Pythagoras Of Samos**
 * http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Pythagoras.html**
 * 2. Pythagoras Biography**
 * http://www.bookrags.com/Pythagoras**
 * 3. The Internet Encyclopedia Of Philosophy: Pythagoras**
 * http://www.utm.edu/research/iep/p/pythagor.htm**
 * 4. Euclid’s Life**
 * http://derrel.net/math/euclid/euclid_life.htm**
 * 5. Biography Of Euclid**
 * http://www.andrews.edu/~calkins/math/biograph/199899/bioeucli.htm**


 * Book**
 * 1. R S Brumbaugh, //__The philosophers of Greece__// (Albany, N.Y., 1981**
 * 2. T L Heath, //__A history of Greek mathematics__// (Oxford, 1931).**
 * 3. L E Navia, //__Pythagoras : An annotated bibliography__// (New York, 1990)**