Wednesday, 20 November 2013

Thales theorem

A very funny way of explaining Thales Theorem:

Dividing a segment into several equal parts
We use Thales theorem to divide a given line segment into a number of equal parts with compass and straightedge or ruler.  By using a compass and straightedge construction, we do this without measuring the line.
    1. Draw the given segment AB. This is the segment that we want to divide.
    2. From point A draw an oblique ray (r).
    3. Chose a measure with your compass and from point A draw arcs on the oblique ray as many arcs as parts you need.
    4. Join the last point of the oblique ray with point B.
    5. Draw parallels using your set square to the segment B7 from the other points on the ray.
Here we have divided the segment in seven parts, but you can divide the segment in as many parts as you need.

I think my construction is easier, but here you have another construction. In the applet we divide it into five parts but it can be any number. You will discover that both are the same!.

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