- Practical advice
- Octagon
- hexagon
- Right angle
- Constitute the first summits
- Extend the rights
- Draw the octagon
- Draw a hexagon
- Draw circle and intersections
- Connect the vertices
- Draw a first axis
- Make a right angle

According to the dictionary, the polygon is a figure closed by segments of the line. Square, diamond, rectangle and triangle are among them, as are their multiples: hexagon, octagon, etc. But if the first are easy to draw, the others claim a little practice.

### Practical advice

The American Pentagon owes its name to the characteristic shape of its building, a classic in military architecture since Vauban. Its layout, more difficult than the other forms, is done with a compass. The method is the same as for a hex except that the reported radius is not that of the main circle. It is obtained from two intermediate reports, which increase the risk of error. Given this difficulty, the form is often discarded, both in decoration and carpentry.

All these figures correspond to precise mathematical formulas. Fortunately, it is not necessary to have a higher degree to achieve them. A compass and a rule are enough for you in all cases.

● The most complex *polygons* are frequently found in decoration, especially with hexagonal tiles from Provence or Dauphiné. The hexagon and octagon are also used for framing, a vanity mirror, for example, and carpentry. In similar applications, many table tops, or some wood floors, are octagonal.

● Hexagons and octagons are, like squares, regular polygons. This means that these figures have sides of the same length and that they fit into a circle connecting their vertices. Hence the use of the compass, but they are their only common points because their methods of drawing differ significantly.

## Octagon

The sides of an octagon are made from two squares, staggered by 45° and inscribed in the main circle. The first square is drawn from two axes that intersect at right angles: its diagonals are equal to the diameter of the circle and pass through its center. The route is reduced to successive postponements made to the rule. The method can be used regardless of the dimensions sought. If this is a table top, replace the ruler with a straight line and use a meter to draw straight lines. Remember to erase the registration axes to avoid cutting errors.

## hexagon

The sides of the hexagon do not de-compose into a simpler geometric figure, except in the triangle. But they are drawn almost entirely to the compass without even changing the spacing, which remains equal to the radius of the main circle. Once the trick is included, it does not take more than two minutes to draw a hexagon, regardless of size. This principle also allows you to draw a 12-sided dodecagon. The rule is actually used only to bring the summits together.

## Right angle

How to check or spot without square a right angle, like the one used to draw an octagon, for example? The problem arises as soon as the dimensions of the piece to be cut are important. The safest method then remains the use of the compass. A straight line and a radius chosen at random are enough to obtain a perfectly square angle (see the last two photos).

## Constitute the first summits

Draw a line AB equal to the width of the desired figure, then a perpendicular CD, of the same length, passing through the center O. The points A, C, B and D constitute the first vertices.

## Extend the rights

Draw one side of this first square, AC, for example. Locate the middle E and draw another straight line from the center O. Extend it to a point F, so as to obtain a segment equal to the radius OA.

## Draw the octagon

Repeat the previous step for all four sides of the first square (CB, BD and DA segments). In the end, you get 8 vertices that can be gathered to make an octagon of the desired size.

*Draw* a hexagon

To draw a hex, draw the main circle A with a compass. Without changing the spacing, prick the tip at any point in the circumference and mark the intersections.

## Draw circle and intersections

Go back to one of these intersections to mark the next, and so on... The game is to go around the circle, with the same spacing, to return to your starting point without delay.

## Connect the vertices

It remains only to connect the vertices, materialized by the intersections, to draw the hexagon. For a dodecagon, carry along the circle a length equal to half a radius only.

## Draw a first axis

To make a right angle without square, draw a first axis AB and locate its center O precisely. Then adjust the distance of your compass so that it corresponds to the length of the axis.

## Make a right angle

Then prick it in A and draw a bow vertically from the center. Repeat the operation from point B, and draw a line from point C to center O: it forms with the axis AB a 90° angle.