The measurement of circles is closely connected to the measurement of angles. This is because the measurement has a rotational aspect; that is, one ray must be turned about the vertex until it coincides with a more static aspect. The circle is the perfect tool for measuring planes of angles, because any angle cuts off the same fractional part of every circle whose center is at the vertex of the angle.

Different Ways to Measure Circles

In degree measure, the circle is divided into 360 equal parts, while in gradient measure, 400 equal parts of a circle are used. Since there are four right angles in a circle, there are 100 gradients in a right angle, making gradients a better fit with the decimal system. Nevertheless, degree measure is the predominant system for measuring angles using fractional parts of a circle.

A different method for measuring angles...