## Rechtlich gesch

POLYGONS

### Definitions

A polygon is a plana figure bounded by more tHan four straight sides. Polygons that are frequently referred to have particular names. Some of these are listed below. A pentagon is a plane figure bounded by five sides. A hexagon is e plane figure bounded by six sides. A heptagon is a plane figure bounded by saven sides. An octagon is a plane figure bounded by eight sides. A nonagon is a plane figure bounded by nine sides A decagon is a plane figure bounded by ten sides. A regular polygon is one that has all its sides equal and therefore all its exterior angles equal and all its interior angles equal.

It is possible to construct a circle within a regular polygon so that ad the sides of the polygon are tangential to that circle. The diameter of that circle is called the diameter of the polygon. If the polygon has an even number of sides, the diameter is the distance between two diametrically opposed faces. This dimension is often called the 'across-flats' dimension

The diagonal of a polygon Is the distance from one comer to the comer furthest away from it. If the polygon has an even number of sides, then this distance is the dimension between two diametrically opposed comers.

Constructions

To construct a regular hexagon given the length of the aidM (Fig. 2/27)

1. Draw a circle, radius equal to the length of the side.

2. From any point on the circumference, step the radius around the circle six times. If your construction is accurate, you will finish at exactly the same place that you started.

3. Connect the six points to form a regular hexagon.

To construct a regular hexagon given the diameter (Fig. 2/28)

This construction, using compasses and straight edge only, is quite feasible but is relatively unimportant What is Important is to recognize that a hexagon can be constructed. given the diameter or across-flats dimension, by drawing tangents to the circle with a 60s set square. This is very importent when drewing hexagonal-headed nuts

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### Responses

• damiano
How to draw hexagon across flats?
8 years ago
• Eliisa
How to construct hexagon using the method across flat?
8 years ago