Circle
Aiton's Encyclopedia (1910)
in geometry, a plane surface bounded by a single curved line, every point of which is equally distant from a point within called the center. Properly speaking the space, not the bounding line is the circle. The saying that one lost in a storm is likely to travel in a circle, meaning to follow a circumference, is an illustration of the difference between popular and scientific language. Naturally enough the circle, one of the fundamental as well as one of the most graceful figures, attracted the attention of the earliest mathematicians. From the Babylonians we have the division of the circumference into 360 equal parts or degrees, and these into sixty minutes each, and the minutes into sixty seconds. Euclid, the Greek mathematician who taught at Alexandria about 277 B. C., enunciated and demonstrated the theorems of the circle in a manner little improved upon in modern textbooks. The problem of squaring the circle, or of finding the dimension of a square which shall be absolutely equivalent to a given circle, has been a standing problem for centuries. It cannot be solved owing to the fact that the relation between the circumference and the diameter cannot be found exactly. The well known ratio of 3.1415926535+ cannot be brought to an end. When one assumes to prove that certain angles are equal, because they are formed by a straight line intersecting parallels, and then undertakes to prove that the lines are parallel, because the angles in question are equal, he is said to argue in a circle.
What Has Changed in the Last Century
The geometry Aiton's set out in 1910 is exactly the geometry taught now: the circle as the region bounded by a curve equidistant from a centre, Euclid's theorems "little improved upon," and the Babylonian 360 degrees still divided into minutes and seconds. On squaring the circle the entry gives the right answer for a slightly loose reason: the impossibility had already been settled in 1882, when Ferdinand von Lindemann proved that pi is transcendental, so no ruler-and-compass construction can produce the equivalent square. The one figure that has moved dramatically is the value itself, given here as 3.1415926535+; computers have since carried pi past 100 trillion decimal places, and it does indeed never end. Modern textbooks are likelier to date Euclid's Alexandrian teaching to about 300 B.C. rather than 277.
Written for this edition, 2026.