Apothem

The term Apothem (Greek ἀπόθεμα "File" ) is in the geometry of a historical name for the solder from the center of a circle to a chord of the circle. The length of the Apothemas is thus the distance of the chord from the center of the circle and equal to the difference between the radius and the height of the tendon that is historically referred to as Sagitta. In a regular polygon inscribed in a circle, all Apothemen are congruent to each other and their lengths correspond to the Inkreisradius of the polygon.

Definition

Is a circle with a center and a chord of the circle with the center, then the apothem of the chord is defined as

So the line connecting the center of the circle and the chordal center. The apothem is so that the solder from the center of the circle on the tendon, with the nadir point is. Besides the track itself is the length of the route, so the distance of the chord from the center of the circle, called the apothem.

Calculation

If the circle radius and the length of the chord, then applies according to the Pythagorean theorem for the length of the Apothemas

And thus

In a regular polygon with sides and the side length, the length of each Apothemas the Inkreisradius of the polygon and thus

Using the Apothemas may also the surface area of a regular polygon as determined as a regular polygon can be decomposed into congruent isosceles triangles of the surface. For a variety of regular polygons, the following values ​​are obtained: