Mathematical Happenings

Greek mathematicians from the 7th Century BC, such as Pythagoras and Euclid are the reasons for our fundamental understanding of mathematic science today. Adopting elements of mathematics from both the Egyptians and the Babylonians while researching and added their own works has lead to important theories and formulas used for all modern mathematics and science.

Pythagoras was born in Samon Greece approximately 569 BC and passed away between 500 – 475 BC in Metapontum, Italy. Pythagoras believed that all things are numbers. He also believed that mathematics was and is the core of everything mathematical. He also believed that geometry is the highest form of mathematics and that the physical world could always be understood through the science of mathematics.

Pythagoreans have and will continue to give recognition to Pythagoras for 1) the angles of a triangle equaling to two right angles. 2) The Pythagoras theorem, which is a right-angled triangle, and the square on the hypotenuse equaling to the sum of the squares on the other two sides. This theory was created and understood years earlier by the Babylonians, however, Pythagoras proved it to be correct. 3) Pythagoras constructed three of the five regular solids. The regular solids are called tetrahedron, cube, octahedron, icosahedron, and dodecahedron. 4) Proving and teaching that the “earth is a sphere in the center of the universe and that the planets, stars, and the universe were spherical because the sphere was the most perfect solid figure numbers. He also taught that the paths of the planets were circular (Douglass, 2005).” Pythagoras was also the first known person to recognize that the morning star and the evening star were in fact the same; planet Venus.

The biggest influence left by Pythagoras was the Pythagorean theorem. This was the first time in history a formula could be used to calculate something using only outside information. This idea and formula eventually developed and lead to the development of Algebra, Trigonometry, and Calculus. The Pythagorean theorem is one of the basic roots to modern mathematical science.

Euclid was born in approximately 330 BC, and passed away in approximately 260 BC. There are no records of his exact birth and death date, as well as no known information about his personal life. However, we do know that Euclid educated people on mathematics in Alexandria, Egypt at the local library. Also, Euclid wrote the most detailed mathematical work of all time, called the Stoicheia or Elements, a thirteen-volume work written in detail compiling geometrical knowledge based on other mathematicians work from the previous 2000 years. Such mathematicians included Thales, Pythagoras, Plato, Eudoxus, Aristotle, Menaechmus and many others,

Euclid believed that 1) “all things, which are equal to the same thing, are also equal to one another. 2) If equals are added to equals, the sums are equal. 3) If equals are subtracted from equals, the remainders are equal. 4) Things that coincide with one another are equal to one another. 5) All right angles are equal. 6) You can extend the line indefinitely. 7) You can draw a circle using any line segment as the radius and one end point as the center. 8) You can draw a straight line between any two points. 9) The whole is greater than the part. 10) The remaining five postulates were related specifically to geometry. 11) You can draw a straight line between any two points. 12) Given a line and a point, you can draw only one line through the point that is parallel to the first line (Douglass, 2007).”

The importance of Euclid is that he developed the discipline and created an organized system and study that allowed for other mathematicians to learn from and continue developing in geometry. For these reasons, Euclid is known as the Father of Geometry.

The 7th Century BC brought us the fundamental roots for development in today’s modern world. The Pythagorean theorem is the foundation of mathematics, and continues to be so studied by mathematicians. In fact, there are currently over 400 different evidences of the Pythagorean theorem, one of which being by President Garfield. Without Euclid and his mathematical work, compiling so many great mathematicians before him into an organized and understood volume of work we would not be as developed and understand the formulas we currently know today.

References

Douglass, C. (2005). Pythagoras. Retrieved from http://www.mathopenref.com/pythagoras.html Douglass, C. (2007). Euclid. Retrieved from http://www.mathopenref.com/euclid.html Lewinter, M., & Widulski, W. (2002). The Saga Of Mathematics. Saddle River, NJ: Prentice Hall. The Story of Mathematics. (2010). GREEK MATHEMATICS. Retrieved from http://www.storyofmathematics.com/greek.html