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Our Tips & Tricks this month are about mathematics. But don't worry, it'll be a very practical approach!

If, let's say, you want to design an octagonal table, freehand drawing is not the best way. It would also be very time-consuming to carry out a comprehensive construction several times in order to reach your aim.

We have another solution for you!

As an example, we have constructed an octagon. But of course, this construction also works for other polygons - whether you wish to construct a heptagon or a pentagon...

Construction of a octagon

The hot tip is the formula

To fix an edge on a table or to calculate the space required per person, you first have to know the length of the edges. There is a simple formula for this, which you won't find in any collection of formulas.

Calculating the length of the edges of a polygonal table:

K = R*2*sin(360°/(2*N))

Formula key

R
the radius of the construction circle (see picture above)
K
the length of the edge
N
the number of edges

At first, you calculate the content of the brackets, save it and calculate the rest.

Now take your calculator or use our online calculator:

Online calculator to calculate the length of the edges


 

And now the other way round? Calculating the radius of a polygonal table

You can also calculate, how many people (with a given edge length) can sit at a table consisting of a certain surface. As a rule of thumb, you should allow for an edge length of 600 mm per adult person.

With the given length of the edge and the number of edges, the following formula applies:

R = K/2*sin(360°/(2*N))

Here is an example calculation:

You have an octagon (see above) and you want to have an edge length of 600 mm:

R = 600/2*sin(360°/(2*8))

R = 783.9377789258259 mm

R = 784 mm

You see, it's really easy! At first, again calculate everything below the horizontal line, and then divide the length of the edge by the result. Or simply use our online calculator in order to calculate the radius.

Online calculator to calculate the radius


 

The final step is the construction.

The geometric construction – Step-by-step explanation

Geometric constructions are easier than you might think. You only need 5 steps:

  1. Draw the construction circle

    At first, draw the construction circle. The best way is to draw it with the radius you have calculated prior to this step. As a tool you can use a self-made compass which is made of a wooden or plastic strip, in which you have drilled a hole for the pencil. The centre is a nail hammered into the base. For precise constructions we recommend using compass heads, for example our Veritas Beam compass heads or our Kunz compass heads.

    As your next step, draw in the central axis.

    Draw the construction circle
  2. Drawing in a section of a rayn

    The next step is drawing in a section of a ray and dividing it into equal proportions. The number of proportions depends on the number of edges you want to have for the polygon. We recommend to use even numbers, because this makes the division easier. The length of the ray and the slope are negligible. Now, connect the top point with the point of intersection and the perpendicular line. All other points will be translated parallel and are also intersected with the central line.

    Drawing in a section of a ray
  3. Calculating the point of intersection

    As your next step, draw two arcs with the diameter (not the radius!) set in the compass. The centre of the circles is the point of intersection of the circle and the perpendicular line.

    Calculating the point of intersection
  4. Drawing in the points of intersection of the circles

    Now connect the points on the central line with the two points of intersection of the circles. Leave out the first point and draw in the second, leave out the third point and draw in the fourth and so on.

    Drawing in the points of intersection of the circles
  5. Connecting the points of intersection

    The points of intersection you have just created from the straight lines are now connected with the construction circle. Now your polygon is done!

    Connecting the points of intersection

For more information, our experts are at your service

Should you have any difficulties when realizing our projects, please do not hesitate to contact us, we will be at your disposal.

You can reach our experts at the following hotline: +49 (0) 991 9109 922.

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