S: The Search for Truth: Pythagoras
FC: How do we know what is true? World History Project on Greece | Pythagoras
1: - a verified or indisputable fact, proposition, or principle
2: Information about Pythagoras | Pythagoras was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He is often referred to as a great mathematician and scientist, but he is best known for the Pythagorean theorem.
3: Pythagoras' Accomplishments | -discovered even and odd numbers -discovered perfect numbers -developed Pythagorean Theorem -discovered triangular numbers -discovered irrational numbers
4: The Search For Truth | Pythagoras and his followers were interested in exploring the principles of mathematics, the concept of mathematical numbers, and the idea of a proof. Their motivation behind trying to find the truth was to understand higher, a divine reality in numerous fields including mathematics and astronomy. By searching for truth through mathematics, the Pythagoreans made important discoveries in different areas of math and science that are both mathematically correct and continue to be used today.
5: Astronomy Pythagoras made many significant discoveries and inferences in the field of astronomy while he was on his search for truth. He hypothesized that the earth was round because of its reflection on the moon. He also hypothesized that all the planets orbited around a central fire. Finally, he hypothesized that the sun and other planets were all spheres along with Earth. | Truth Over Time All of Pythagoras' inferences have stayed the same and have been proved to be correct. They are the basis of our interaction with space and allow us to understand the ways of the universe.
6: Music | Pythagoras made several interesting conclusions in the field of music. He believed that mathematics and music were very closely related and that each music note had an exact ratio in math. He observed that vibrating instruments produce harmonious sounds when the ratios of the lengths of the instruments were whole numbers. He came to this conclusion when he heard the harmonious sounds of a local blacksmith shop and discovered that the hammers were all of perfect ratio sizes. | Truth Over Time This conclusion has been proved false over time because of the fact that these perfect ratios are only relevant to string length and not to hammer weight or length. Therefore it does not apply to all music, only certain stringed instruments.
7: Math | Pythagoras made the most conclusions in the field of math. One of those conclusions was on number theory. The Pythagoreans applied varying qualities to different numbers, each one having a character and property of its own. They believed that numbers were physical entities that were the physical components of everything in existence. In addition, The Pythagoreans are credited with the construction of the five regular solids. The Pythagoreans also discovered the idea of dimensions in terms of geometry throughout the world. They proved that the sum of the interior angles of a triangle is equal to 180 degrees. Another discovery was the existence of irrational numbers in mathematics. However, the Pythagoreans’ most famous discovery was the Pythagorean Theorem. The Pythagorean Theorem states that “In any right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the long side.” The Pythagoreans discovered this theorem through geometrical means, by arranging triangles in various ways to prove the conclusion. The formula for the Pythagorean Theorem is A^2 + B^2 = C^2, with A and B being the shorter sides and C being the longest side, or hypotenuse, of the triangle. Pythagoras was not the first person to discover the theorem, but he was the first one who was able to prove it. | Truth Over Time All of Pythagoras' theorems and conclusions except for one have been proved to be correct and are used in mathematics all over the world. His one conclusion that was not proved, that numbers have physical properties, was deemed incorrect and decided that numbers only relate to math, not the entire world. But Pythagoras' other conclusions have all been proved and continue to be used to solve problems in both practical life and in math. The Pythagorean Theorem is now the most important formula when talking about triangles and is used in countless proofs throughout math.
8: Final Thoughts | In | In conclusion, the majority of the truth that Pythagoras found has stayed true throughout time. Many of his theorems and ideas continue to be used today and are applied in many fields including astronomy and mathematics. His theories are the basis for much of geometry and his legacy will live forever because of his discovery of the truth.
9: Consequences | d | Positive: -made contributions to Geometry -discovered the Pythagorean Theorem -helped society gain an understanding of Outer Space -was basis for future searches for truth in the fields of astronomy and mathematics Negative: -people became jealous and often attacked him or his religious buildings -was considered mentally ill by some because of his extreme views about astronomy
10: Citations | 1.http://www.storyofmathematics.com/images2/pythagoras_music.gif 2.http://www.crystalinks.com/pythagsun.gif 3.http://utnsliteracy.pbworks.com/f/1256058634/pythag_thm.gif 4.http://mrfazio.edublogs.org/files/2011/10/pythagorean-theorem-16l2i95.jpg 5.http://home.wlu.edu/~mahonj/Ancient_Philosophers/Pythagoras4.jpg 6.http://s3.amazonaws.com/files.posterous.com/soulache/gz498F9y3xIb7TBBBDmTeVS9f1wejNTazjXKvridxtWWMrcJEWqkkaVGKkg1/truth.gif?AWSAccessKeyId=AKIAJFZAE65UYRT34AOQ&Expires=1328476850&Signature=W2rinvIq1eAO5B%2FhfoGIzagvcdA%3D 7.http://edu.glogster.com/media/5/27/29/31/27293175.jpg 8.http://2.bp.blogspot.com/_SKXGBUeUyQs/SW646vpLZhI/AAAAAAAAAQk/D4hAvxuFiDE/s400/PythagoreanTheorem.gif 9.http://natureofmathematics.files.wordpress.com/2010/05/pythagoras_statue.jpg 10.http://practicalphysics.com/imageLibrary/jpeg463/1932.jpg
11: The End!