Definition:Circle/Semicircle

Definition

In the words of Euclid:

A semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle.

(The Elements: Book $\text{I}$: Definition $18$)

In the above diagram, the region bounded by the straight line segment $CD$ and the arc $DBC$ is a semicircle.

Also, the region bounded by the straight line segment $CD$ and the arc $DFEC$ is a semicircle.

Center of Semicircle

The center of a semicircle is defined as being the same as the center of the circle from which the semicircle is taken.

Diameter

The diameter of a semicircle is the diameter of the circle from which the semicircle is derived.

Also known as

A semicircle is also seen referred to as a hemicycle, but this is uncommon.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hemicycle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): semicircle