What is a Circle? From the tires on your cars, the ring on your finger,
to the math assignment you still haven't completed that talks about the area
of a circle, circles circumference you.
A Circle is a closed plane curve consisting of all points at a given distance
from a point within it called the center. It is one of the fundamental shapes
in geometry, and one of the most widely seen and used. Circles today are used
not only in your math classrooms but also in architecture, religious and psychological
symbolism, art, and metaphorical phrases. (Coxeter, 1967) (See above link for more
details on how circles are used.)
Where did circles begin, how did they start, who first discovered them? According to
record, circles have no known beginning or end. There is no record to show the first
“discovered circle.” It is commonly thought among anthropologists that circles early
on were not used as mathematical elements, but rather were symbolic of life, unity,
and the balance of nature. (Heath, 1921) The Sun was the source of all life, and the
ultimate circle that represented these characteristics. Circles were later used as
more than symbolism, as was the case with the wheel in the Neolithic Age dating back
to about 9500 BC. (Heath, 1921)
One of the oldest recorded circle designs is found in England at Stonehenge Wiltshire.
This structure was built in approximately 4000 BC. This ancient structure is thought
to have had spiritual meaning and was built as an astronomical observatory. Circles
were often used for astronomical purposes by the ancient Egyptians and Greeks. Many
believed that something divine or perfect could be found in a circle. (Howard, 1997)
Between 1680 BC and 1620 BC, Ahmes, an Egyptian scribe, wrote in his famous Rhind Papyrus
Problem 50 which states a solution to finding the area of a circle given only
the diameter. Ahmes concludes that the area is 64/81d^2 which can be written in
modern form as 256/81r^2. 256/81 equals approximately 3.16, or roughly p.
(Eisenlohr, 1877)
In 650 BC the first theorems were recorded by Thales, a Greek philosopher, scientist
and mathematician. Two of his five theorems related to circles which were: “A circle
is bisected by its diameter, and Thale’s Theorem: any angle inscribed in a semicircle
is a right angle.“ (Heath, 1921)
Euclid of Alexandria in about 300BC in Book III of Euclid’s Elements wrote about how
inscribed and circumscribed polygons used to describe
properties of circles.
Anaxagoras, a Greek mathematician in 450 BC, began working on a problem known today
as ‘Squaring a circle.’ This problem, which in 1882 was
proven impossible
to accomplish, involved
trying to find a square with the same area as a circle. (Sander, 1993)
The history of circles is a never-ending story that grows with each new discovery.
The study of circles has lead to the development of geometry and calculus. Circles
will always hold their symbolic meaning of unity, life, and the balance of nature.
Circles will continue to help us write and make history.
