Happy π-Day: What is Pi?

What is π, or “pi” as we spell it out. The mathematical definition is the ratio of a circle's circumference to its diameter:

It is one of many mathematical constant. Commonly reffered to the value 3.14, which is inaccurate to say it mildly. Contrary to popular belief, π wasn’t discovered by a greek philosopher. Some of its earliest references are from Babylon and ancient Egypts, accurately enough calculated at the time. A babylonian clay tablet dated 1900-1600 BC used the following approximation:

In the Egyptian Rhind Papyrus dated around 1650 BC, which is a copy from another papyrus dated to 1850 BC, the formula is treated as:

These approximations was close enough at the time.

The knowledge about this had, probably through trade, reached China by mid-first millennium, where its accuracy had been calculated to seven decimal places.

Now let us head over to Grece and fast forward a little, approximately to the year 250 BC. The greek mathematician Archimedes created an algorithm to calculate π through the use of polygons. Basically draw a circle with diameter 1, draw a square around it where the edges touches but not intersects circumference, draw another square inside the circle where the corners touches the circumference. Ok, this didn’t give a good answer, but it give you an idea of how the game goes. By comparing the perimeters of the polygons he could find that π was in between these numbers. Archimedes added sides to this polygon until he reached a 96-sided regular polygon, and calculated the perimeters of these polygons:

In decimal numbers:

This stood the test as the true value of the constant for a very long time. π was hard to calculate any further before mechanical and later electronic calculators came in as aid. Since any other approach to solve π except the polygonic algorithm approach required advanced calculations to the n^th decimal.

Because of the size of the number, let us present it in hexadecimal (base 16) 3.243F 6A88 85A3 08D3 1319 ...

Some ancient cultures used a sexogesimal number system (base 60), the number π would then be represented as 3;8,29,44,0,47. Mark that each of the decimal numbers would have its own symbol.

Happy π-day.