Archimedes’ Constant

3.14159265359…

Episode #1 of the course “Most important numbers in the world”

For centuries, ancient mathematicians and engineers would attempt to build and construct using circles, and they found they needed to accurately calculate the relationship (or ratio) between the distance around the outside of a circle (its circumference) and the distance directly across it through the middle (its “diameter”). The relationship seemed to repeat itself in a pattern, no matter the size of circle, and there were multiple attempts to pinpoint the exact number that represented the ratio. Ancient Egyptians used a rough approximation between 3.12 and 3.16. Ancient Hebrews estimated at 3. But it was the ancient Chinese mathematicians, and later those in India, who were able to calculate the ratio up to an accuracy of 7 digits.

In Europe, Greek mathematician Archimedes in the 3rd century BCE proved the upper limit of the ratio as 22/7, and this value became the commonly accepted number to calculate the circumference to diameter relationship for over 1,000 years. In 1630, the number was expanded to 39 digits, getting closer to its more commonly accepted modern form. It is now understood as an irrational number, which does not end or fall into a repeating pattern.

In the 18th century the Greek letter pi (π) came to signify the relationship and is common in calculations not only of circles, but of ellipses and cosmological curvilinear shapes as well. In common schoolhouse geometry, pi is generally taught as 3.14159 to introductory students. For advanced calculations requiring the utmost precision, values of pi may be taken to hundreds of places in statistics, thermodynamics, cosmology, and electromagnetism.

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