Heptagon like many diagonals

Diagonals in regular polygons

This chapter is devoted to Number and length of diagonals of regular polygons as well as the arithmetic determination of the number of this diagonal.

Number of diagonals:

Under one diagonal one understands in the plane geometry the Connection route from non-adjacent corner points.

Thus, depending on the number of corner points, polygons have different numbers of diagonals.

At a triangle there are only adjacent corner points, so this has a geometric surface no diagonals.

In one square 2 opposite corner points can be connected to each other; thus has a square two diagonals.

Looking at a pentagon, you can see that the number of diagonals increases exponentially, because here you can already five diagonals are drawn.

In one hexagon can be nine diagonals draw in, etc.

Length of the diagonals:

The diagonals of one regular quadrilateral and regular pentagon are each of the same length.

For Polygons with more than five corner points, this knowledge applies Not! Here the diagonals have different lengths.

Calculate the number of diagonals:

The number of diagonals of a (regular) polygon with tease can be done with the help of the following formula determine arithmetically:

This results in the following number of diagonals for polygons:

tease d diagonals
30
42
55
69
714
820
9 27
1035
1144
1254
1365
1477
1590
Diagonals in regular polygons

Under Diagonals one understands in the plane geometry Connections from non-adjacent corner points.

The Number of diagonals of a (regular) polygon with tease can be done with the help of the following formula determine arithmetically: