Definition:Solid Angle/Polygon

Definition

A solid angle described by a polygon is a solid angle whose closed plane curve through which the half-lines pass is a polygon.

In the words of Euclid:

A solid angle is the inclination constituted by more than two lines which meet one another and are not in the same surface, towards all the lines.
Otherwise: A solid angle is that which is contained by more than two plane angles which are not in the same plane and are constructed to one point.

(The Elements: Book $\text{XI}$: Definition $11$)

Containment of Solid Angle

The plane angles which together form a solid angle are said to contain that solid angle.

Vertex of Solid Angle

The common point through which pass the copunctal half-lines describing a solid angle is known as the vertex of that solid angle.

Also see

• Results about solid angles can be found here.

Souces

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): solid angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): solid angle