He went from a 12-gon to a 24-gon to a 48-gon and finally to a 96-gon. He continued visualizing the doubling of sides. This was the critical step that would differentiate Archimedes’ method from those who proceeded him. His brilliance as a Mathematician became apparent as he derived an algorithm that would enable him to use the first polygon with n-sides to calculate the perimeter of the second polygon with 2n-sides. Archimedes decided to double the sides of each polygon (12-gon) thereby reducing the amount of area between circumference and the perimeters. However, there was too much area left between the circumference of the circle and the perimeter of each polygon. Archimedes now had a range of values that would approximate π. The circle, with circumference π, was now between the two polygons. Next, he circumscribed a hexagon about (outside) the circle and used calculations found from the inscribed hexagon to arrive at the perimeter of the outside hexagon. He then conjectured that the hexagon’s perimeter would approach the circumference of the circle (π). Hence, with ½ as a radius, the circumference of his circle would be π. He would be the first to theoretically calculate the digits of Pi.Īrchimedes envisioned a hexagon inscribed within a circle with radius ½. These principles had yet to be printed in a mathematics textbook nor had they been established as areas of mathematics. The idea, called the Exhaustion Principle, would use principles from geometry, trigonometry, and calculus. All of these were approximations of measurements that compared the circumference of a circle to its diameter.Īround 250 BC, a brilliant mathematician by the name of Archimedes of Syracuse became interested in an idea developed by his compatriots a hundred years or so earlier. The Egyptians thought it to be around 3.165. The Babylonians thought Pi to be about 3.125. That relationship was represented by the ratio of the circumference of a circle to its diameter, ultimately referred to as Pi (π). It was not long before each civilization recognized that there was a constant relationship between the circumference of a circle and its longest chord, also known as the diameter. Whether it is myth or fact, there are stories of ‘rope stretchers’ slinging their braids around a circle and then recording the length of the rope as a representation of the circumference. They were focused on how to measure the circumference and area of circles. Yes, there were civilizations, the Babylonians, Egyptians, and Chinese, all unbeknownst to the other, thinking about an original idea related to circles. This was the way of the world circa 1650-1600 BC. Now that you’ve quieted your mind, imagine an original idea and wonder if anyone else in all of civilization is pondering the same thought. You know the noise: social media, earbuds, TV, radio, telephone and more. Like the number Pi, his influence lives on FOREVERĬlose your eyes. Employment and Internship Opportunities.
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