Realization

The number pi, a constant in math and, like the Pythagorean theorem, an example of the universality of forms, was not arrived at by insight.

The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for pi, which is a closer approximation.

In the Rhind Papyrus (ca.1650 BC) the Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for pi.

And from the Old Testament: "Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about." (II Chronicles 4:2) Some authors claim this passage as evidence that the ancient Hebrews used a value of 3 for pi. This passage occurs as part of a description of the building of Solomon's temple, and all the measurements in it are very round numbers, so perhaps this was not meant to be more than a rough estimate.

Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world, approximated the area of a circle by using multiple polygons of known areas and circumference. Archimedes knew that he had not found the value of pi but only an approximation within those limits. In this way, Archimedes showed that pi is between 3 1/7 and 3 10/71.

A universal truth was found step by step, approximation after approximation, over millennia. Yet, even at the beginning, its existence was known.