10182

# The Eratosthenes Machine for Finding the Cube Root of Two

This Demonstration shows Eratosthenes's machine for finding two mean proportionals; that is, given lines and , find and such that . If and , the solution is . Let the lengths of and be 2 and 1, respectively. Move the second and third triangles so that points and lie on the straight line , giving the length of as (approximately 1.25992…).
Eratosthenes's machine consists of a parallel frame and three congruent triangles. Let and . Move the triangles on the right so that and are on the line . By similarity .

### DETAILS

The problem of doubling the cube was to find by ruler and compass, which was proved impossible [1]. This Demonstration shows a solution by sliding a line, which is not an allowable operation in a construction by ruler and compass.
Reference
[1] J. J. O'Connor and E. F. Robertson. "Doubling the Cube." MacTutor History of Mathematics archive. (Jun 26, 2012) www-history.mcs.st-and.ac.uk/HistTopics/Doubling_the_cube.html.

### 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.