Circular Reasoning

In some ways the circle is more basic to universal knowledge than the straight line.  More specifically, the curved line is most often incorporated in the art of toddlers given a crayon.  The youngster will rarely draw straight lines, but he will draw rough circles (ovals) as he doodles.

When he gets curious, he "looks around" and "goes in circles" to take as much of his world in as he can.  The space near him is "around" him and he is "surrounded" with things in every direction. To take it all in he goes in "circles."  The word "round" descends from the Latin word "rota," from which we get "rotate."  The word "circle" comes from the Latin "circulus," the diminutive of "circus" which it borrowed from the Greek "kirkos" which means "ring."

Even in ancient times, the Romans and Greeks built stadiums that were semi-circular or fully round (oval tracks).  They were built in such a way as to give a  view to as many people as possible.  And so, they built "circles."  The methodology naturally would have begun with the architect stretching a measuring line to the optimum distance and rotating the desired arch -- all the way to a circle.  On paper, the "circus" was a lot smaller, and thus a "circulus."

This line became known as the radius.  The resulting line forming the ring turned out to be about six and a quarter times radius (a bit over 6.28).  The radius, when doubled, became the diameter of the circle. The ratio between the widest part of the circle and the distance around it is an irrational number known as "pi" estimated as "3.14" or "22/7".  The area inside a circle is pi times the square of the radius.

The most ancient system of measuring the outside of a circle used what we call quadrants: the four directions measured by fixed points.  The common points were the sunrise and the sunset at the equinox.  The ancient Hebrews used East as forward, making that which was on the left "north" and tha which on the right "south."  Behind them was the unpassable sea, the "west" and sundown.  This way the circle has been divided into 16 common directions we know today.  However, this is not precise enough over long distances, so "degrees" of the arch use "base 60" with 60 times 60, or 360 degrees divided by "minutes" and "seconds."  For convenience, time also follows this scheme.

By the way, 360 is the result of multiplying 3,4,5 and 6 together. Seen as prime factors, this is 2*2*2*3*3*5.  This makes the factors of 360 a long list: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 54, 60, 90, 120 and 180.  All in all, the ancient math guys had it together.

So, What do I know?

The radius is a straight line used from a center point to inscribe a circle.

The diameter of a circle is twice the length of the radius.

The distance around the circle is about 3.1416 times the diameter and about 6.2832 times that of the radius. This is the ratio known as "pi".

The area inside the circle is pi (about three and a seventh) times the square of the radius.