 # Concurrent Diagonals in a 30-Gon Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

When three lines meet at a point, they are concurrent. For the diagonals of a 30-gon, out of the 16801 intersection points, there are 3001 points where three or more lines intersect, with 193 different ways to select three concurrent diagonals.

[more]

Consider six points that divide a circle into arcs . If , then the three lines connecting opposing points are concurrent . This property was used to find the sets of lines. By the pizza theorem, half the circle is covered by wedges , and half by wedges .

[less]

Contributed by: Ed Pegg Jr (November 2015)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

In the initialization, {1,3,9,4,8,5,14} is a sample dataset (selected triple 102). The first six numbers are a partition of 30; the last number is the sector of the 30-gon where the intersection occurs.

References

 B. Poonen and M. Rubinstein, "The Number of Intersection Points Made by the Diagonals of a Regular Polygon," arxiv.org/abs/math/9508209.

 Wikipedia. "Pizza Theorem." (Nov 13, 2015) en.wikipedia.org/wiki/Pizza_theorem.

## Permanent Citation

Ed Pegg Jr

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send