# The locust

The usual paradigm for Euclidean geometry is that one can do every construction with a ruler and a compass. The obvious construction is that of a triangle from three given side lengths. However it turns out that it is sufficient in Euclidean geometry if one requests that one can construct any **isosceles triangle **(a triangle with two legs of same length).

Based on the parallel axiom one can then construct every triangle from its three given side lengths. One starts from points 1 and 2 for the base line* a* , point 3 gives the length of another side

**by its distance to point 1 , point 4 gives the length of the third side**

*b***by its distance to point 2. For obvious reasons the construction for point 28 is called**

*c***locustition**.