Pythagoras of Samos

1. Pythagoras of Samos An Interactive History

2. Introduction This presentation is an interactive history of Pythagoras the famous Greek mathematician. You can skip to any portion of this presentation simply by clicking on the topic you would like to read about; if you would like to follow the presentation through from beginning to end simply continue clicking the next button when you are done reviewing the material. There are also sections of the presentation with blue hypertext that will take you to other pages within the presentation or to external links to supplement the presentation. To begin the presentation click the button at the bottom of the slide.

3. Presentation Menu • History of the person • Fact Sheet • Biography • Pythagorean Cult • Accomplishments • Pythagorean theorem • Platonic solids • Modern Applications • Pythagorean theorem • Platonic solids • Conclusion • References

4. History of the Person Pythagoras was an person who amazed everyone he meat from childhood well into his adulthood. He studied under some of the greatest teachers and discovered some of the most intricate aspects that modern mathematics is built upon. The following pages talk about Pythagoras’s life more so than the mathematics he and his cult discovered. This is not and all inclusive biography however it is a highlight of some of the main points of his life. Menu

5. Fact Sheet • Lived 560 -480 BC • Greek • Mathematician & Philosopher • Pythagorean Cult • Irrational Numbers • Pythagorean Theorem • Platonic solids Menu

6. Biography Known as "the father of numbers", Pythagoras made influential contributions to Greek philosophy and religious teaching in the late 6th century BC. Because legend and confusion cloud his work, little can be said with confidence about his life and teachings. What we do know is that in 560 BC Mnesarchus and Parthenis had a son whom they named Pythagoras and Even as a young child he amazed everyone who met him with his far reaching insight and wisdom. Additionally, we know that Pythagoras was born on the island of Samos. As a young man, he left Samos for Croton in Italy to escape the authoritarian government of Polycrates. Many historians claim Pythagoras visited and studied under the sages of Egypt and of Babylon who were the teachers of other great mathematicians before he went west these accounts cannot be substantiated by historical records and are looked at with some skepticism. It’s said that Pythagoras admired Thales and Anaximander who upon meeting him was advised to go to Egypt to study with the masters of Thales because of his superior wisdom. The next twenty years of Pythagoras’s life was spent perfecting his mathematical abilities in the tutor of one of Thales’s teachers where at the end of his studies he was initiated into the Egyptian Mysteries. Then Pythagoras traveled to Croton Italy where Pythagoras undertook a reform of the cultural life. He urged the people to follow virtue and form a circle of followers around him who would become the Pythagoreans. The Pythagoreans were considered a cult of mathematicians but in reality, they were a school of philosophers and mathematicians. He opened his school to all who wanted to study what he perceived as pure logic of mathematics. This is where is greatest work was done, in the cult of the Pythagoreans. To learn more about Pythagoras as a person click here Menu

7. Pythagorean Cult The Pythagoras and his students believed that everything was related to mathematics, and felt that everything could be predicted and measured in rhythmic cycles through mathematics. Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. Perhaps the mystical side is what lead the group in its envevors to explain the proportionalities of the sides of triangles and consequently finding the number which is an irrational number and by the Pythagorians profession could not exist. This discovery was a closely guarded secret and any member of the Pythagorians who mentioned this finding was killed or disappeared mysteriously. This number was later exaplined by other mathematitians and the huge discovery was broken and as you know today the irrational numbers play an enormous role in modern mathematics. To learn more about the Pythagorean Cult click here Menu

8. Accomplishments It is generally agreed by both historians and mathematicians that Pythagoras can be credited with two major discoveries. The first of which is the Pythagorean Theorem. The accreditation has some skepticism attached to it because some scholars believe that members or the Pythagorean cult were partially responsible for the discovery and that Pythagoras himself possibly was not involved as previously believed. The second accomplishment Pythagoras is accredited with is the discovery of construction of the regular solids known today as the Platonic solids. Menu

9. Pythagorean theorem The theorem states: the sum of the areas of the squares on the legs of a right triangle is equal to the area of the square on the hypotenuse. We are most familiar with the form a²+b²=c². As you can see by solving this puzzle the Pythagoreans ran into a problem when they discovered Pythagoras’s constant of To learn more click here Menu

10. Platonic solids The Platonic solids, also called the regular solids or regular polyhedral. An Example of this would be a cube which we know is basically a three dimensional square. In a platonic solid all the faces of the object have the same area and the sides lengths are also equal. There are only five such figures which are the cube, dodecahedron, icosahedrons, octahedron, and tetrahedron and are shown to the right of the text with their open faced pictorials as well as their end plot graphs. To learn more click here Menu

11. Modern Applications The benefits of what Pythagoras and the Pythagoreans accomplished may not me immediately apparent to you however lets take a closer look at what modern applications his work in developing the Pythagorean Theorem and the discovery of the platonic solids has had on our lives. Menu

12. Pythagorean theorem This has had a huge impact on the civil engineering aspect of history. With this theorem calculations can be easily made for grade lengths of roads and heights of large immeasurable objects now become measurable. More impressively Albert Einstein used the Pythagorean Theorem to explain his theory of special relativity for objects such as particles moving at extremely high rates of speed. Menu

13. Platonic solids The purpose of platonic solids was not obvious to their discovers however, now we use these facts in modern chemistry for determining how chemical bonds will form and the atomic structures or compounds and atoms. Platonic solids have had a huge influence on the field of chemistry and was also used in astronomy by Johannes Kepler to attempt to explain the universe 1900 years after Pythagoras died. Menu

14. Conclusion Pythagoras was a man who amazed people from the beginning of his life until the end. His contributions to mathematics has made many things in modern life available. His views and philosophy founded Pythagoreans a mathematical cult who aided in the discovery of one of the most well known and used theorems in mathematics still today. Without the Pythagorean Theorem Albert Einstein would not have been able to calculate special relativity and modern science would be considerably more antiquated. Pythagoras is also credited with the discovery of irrational number through the discovery of his self named theorem. The discovery of irrational numbers was not covered in this presentation however without irrational number we would not have been able to build computers or have advanced medicines. The discovery of the platonic solids also laid the foundation for modern chemistry which also has developed modern medicine as well as taking man into space. The efforts of one man between 560 and 480 BC helped build the mathematical foundation needed 2565 years later– tell me that is not amazing. Menu

15. References • Science World • Wikipedia • Eric W. Weisstein. "Platonic Solid.“ To exit the presentation click the exit button Exit Presentation Menu