# Becker's curve

- Author:
- RMF

Construction of Becker's curve in a semicircle of diameter AG. Steps to find a point K of the curve from a point F of the semicircle:

- Semicircle of diameter AG (see diagram).
- A point F on the large semicircle is selected and FG.
- FL is perpendicular to AG.
- Semicircle of diameter AL.
- K is the intersection of AF with the semicircle AL.

Once the curve is drawn, it is easy to prove that AG/AF = AF/AL = AL/AK: it is enough to show that triangles AGF and ALK and semicircles form an Archytas' triangle. Therefore, AKFGL is an Archytas' solution. Becker's curve is the same curve as Viviani (and Knorr), but its definition is different. That definition is the most fitted to the Archytas' construction, and Becker was aware of the fact that it "directly ties in with the planimetrical core piece of solution of Archytas".