10178

# Iterated Subdivision of a Triangle

This Demonstration shows the repeated subdivision of a triangle.
The barycenter of the triangle is determined using the classical dot product between the masses and the vectors of their positions:
The division into six triangles is done by using the barycenter as the common vertex and dividing the three edges according to the divider ratios .
A multitude of shapes can be achieved by iterating this process times and moving the sliders. This way, one creates triangles. The barycenter of each triangle can be moved by dragging the locators and varying the weight sliders. The shape of the triangles can be altered with the three divider sliders. Starting with a symmetric initial triangle gives a more balanced end result.

### DETAILS

Homogeneous barycentric coordinates are used by assuring that
A purely barycentric subdivision is given in snapshot 1 by setting all three masses to 0.333 and all three dividers to 0.5.

### 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.