11428

# Concurrent Diagonals in a 30-Gon

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.
Consider six points that divide a circle into arcs . If , then the three lines connecting opposing points are concurrent [1]. 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 .

### 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
[1] B. Poonen and M. Rubinstein, "The Number of Intersection Points Made by the Diagonals of a Regular Polygon," arxiv.org/abs/math/9508209.
[2] Wikipedia. "Pizza Theorem." (Nov 13, 2015) en.wikipedia.org/wiki/Pizza_theorem.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.