## Dividing a Segment into N parts:

Besteman Construction II

A Mathematical Droodle: What Is This About?

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Copyright © 1996-2018 Alexander Bogomolny## Dividing a Segment into N parts:

Besteman Construction II

The applet illustrates an algorithm for dividing a segment in N equal parts found by a college student, Nathan Besteman, and reported in the recent issue of *Mathematics Teacher*.

What if applet does not run? |

The construction employs a well known property of angle bisectors in a triangle. In ΔACD, let DP be the angle bisector of angle D. Then

(1) | AP/PC = AD/CD |

It follows from (1) that if CD = N·AD, then

### References

- N. Besteman and J. Ferdinands,
__Another Way to Divide a Line Segment into__,*n*Equal Parts*Mathematics Teacher*, Vol. 98, No. 6 (Feb. 2005), pp. 428-433

- How to divide a segment into n equal parts
- Al-Nayrizi's Construction
- Besteman's Construction
- Besteman Construction II
- Dividing a Segment by Paper Folding
- Euclid's Segment Division
- The GLaD Construction
- The SaRD Construction
- Similar Right Triangles
- Divide Triangle by Lines Parallel to Base

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