Detective Archimedes: The Case of a Lifetime
By Adrianna Anderson
Detective Archimedes, a famous mathematics investigator, was on the case of a lifetime. He lived in Greece and studied for many years to become an expert in physics, engineering, astronomy, and mathematics. So when he was approached by the department to take on a special mathematics case that could make history, he couldn’t turn it down.
His case was to uncover the mystery of the circle. The mystery of the circle was more daunting than those of other shapes, like rectangles. Finding the area and perimeter of a rectangle was a cakewalk compared to this case. A knucklehead with a ruler could figure that one out. No, this case was the BIG-ONE!
Mathematicians for years and years had racked their brains trying to uncover truths about the circle. Several investigators came close to the truth.
The Ancient Babylonians tried calculating the area of a circle by using an equation that squared the radius and multiplied that by 3. Ancient Egypt also shed light on the area of the circle by multiplying the radius squared by 3.1605 in The Rhind Papyrus (ca. 1650 BC). In their investigations they discovered that there was a link between every circle. There was a pattern, a rule, that makes a circle a circle.
But everyone realized 3 and 3.1605 just didn’t cut it. There was a mystery number that needed to go in the equation that was close to 3 but they needed a more accurate number. That’s where Detective Archimedes came into play. He was destined to discover this magic number that determines a circle. So Archimedes went to work. He decided to apply some of the great discoveries of another renowned mathematician, named Pythagoras .
Pythagoras was known for a theorem by his namesake that was about triangles. The Pythagorean Theorem is what would help Archimedes solve his case.
Detective Archimedes inscribed a polygon (broken up into triangles) in a circle and another polygon circumscribed around the circle. He was able to calculate the areas of the polygons using Pythagorean Theorem. The more sides added to the polygon the closer it got to a circle. This allowed him to get closer to calculating the area of the circle and thereby an approximation for the magic number. His approximation of 3 1/7 was the closest anyone had ever come.
The magic number mathematicians had worked on for centuries was an irrational number , 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ... you get the point.
The knowledge of circles laid down before him by other mathematics detectives paved the way for Archimedes to discover the magic number, the pattern, the rule to every circle.
Years later, this number was given a Greek name, perhaps in honor of Archimedes, the Greek mathematician. It is now called ∏ (pi). Now we can find the circumference and area of any circle with ease using the circumference formula (C = ∏d) and the area formula (A = ∏r²).
Thus concludes the tale of Detective Archimedes and the case of his lifetime.
This story was based on true events.
References
Exploratorium. (2013). A brief history of pi. Retreived on May 31, 2013 from http://www.exploratorium.edu/pi/history_of_pi/index.html
Mastin, L. (2010). The story of mathermatics: Hellenistic mathematics- Archimedes. Retrieved on May 31, 2013 from http://www.storyofmathematics.com/hellenistic_archimedes.html
Merriam-Webster.com. (2011). Retrieved May 8, 2011, from http://www.merriam-webster.com/dictionary/
All images were created by Adrianna Anderson.