Greek Mathematics, Essay Example

In ancient Greece, some of the greatest cultural advances came about in geometry, mostly through the ideas and principles of Euclid who made revolutionary progress in the analysis of two and three dimensional space and forms, thus bringing about the mathematical field of Euclidean geometry. There was also Pythagoras who believed that the entire world could be explained through the use of numbers. His mathematical principles which led to the creation of the Pythagorean theorem inspired other Greek thinkers to explore mathematics and its place in the natural world.

In Plato’s Meno, described by Laurence Barker as a dialog or conversation between the Greek philosopher Socrates and Meno, a prominent Athenian and well-schooled in the Greek classics (“The Duplication of the Square,” 2). In one section of the Meno, Socrates poses a mathematical question to a slave boy owned by Meno. Basically, this problem can be explained as thus–if you have a square (regardless of its dimensions), how do you create a new square whose area is double that of the original square? As Barker points out, this can be done by drawing a diagonal line in the original square from the top left corner to the bottom right corner and then extending the lines outward from the corners, thereby creating another square with double the area of the original square (“The Duplication of the Square,” 1).

Also, the original square with a line drawn from the top left corner to the bottom right corner divides the square into two equal parts or right triangles. However, the other square contains four right triangles which can be created by drawing a line from the left corner to the right corner of the second square and a line from the top corner to the bottom corner. Mathematically, this problem is based on geometry or more accurately, on the Pythagorean theorem, due to the four right triangles bearing a hypotenuse or the longest side of a right triangle.

This type of mathematical problem or geometrical expression can be found in many other cultures and societies that existed alongside that of the ancient Greeks and those that came long before them. For example, Babylonian mathematics used an  approach very similar to that of Socrates and Pythagoras as can be seen in Figure 6 of Hodgkin’s History of Mathematics: From Mesopotamia to Modernity. Image A shows a cuneiform tablet that describes the square root of 2 and is inscribed as a square tipped to one side, much like a diamond, with a horizontal line and a vertical line dividing the square into four equal segments or right triangles. Obviously, Babylonian mathematicians were thinking along the same geometrical lines as Socrates and Pythagoras (25).

Also, in the culture of ancient India around 600 B.C.E., there are examples of the use of geometry similar in nature to that of the ancient Greeks and Babylonians as found in the Vedas, such as descriptions close to the Pythagorean theorem and approaches for figuring out the length of the diagonal of a square, the amount of surface area, and the volume of solid figures like cubes and cylinders (Berlinghoff & Gouvea, 14). According to Berlinghoff and Gouvea, there is plenty of evidence in the archeological record that demonstrates mathematical awareness of the Pythagorean theorem in places like Mesopotamia (Babylonia and Sumer), ancient Egypt (think of the Great Pyramid), and China (Math Through the Ages, 139).

Perhaps the greatest mathematicians were the ancient Egyptians whom Herodotus describes as being the inventors of geometry. One area in which the ancient Egyptians used geometry was in land measurement in order to construct the foundations of buildings, temples, and the Great Pyramid whose base is a square and can be divided into two right triangles (Monaldi, 1). Therefore, the differences between Greek mathematics and that of other cultures is minimal, meaning that there is far more similarity than difference which goes to show that the fundamentals of geometry were known everywhere in the ancient world.

Works Cited

Barker, Laurence. “The Duplication of the Square in Plato’s Meno.” Web. 2006. Accessed 20 October 2012. http://www.fen.bilkent.edu.tr/~barker/menojul.pdf

Berlinghoff, William P., & Fernando Q. Gouvea. Math Through the Ages: A Gentle History for Teachers and Others. Farmington, ME: Oxton House, 2004.

Hodgkin, Luke. History of Mathematics: From Mesopotamia to Modernity. UK: Oxford University Press, 2005.

Monaldi, D. What Do We Know About Egyptian Mathematics? The Nature and Growth of Ideas in Mathematics, 2012.