11481

# Lill's Graphic Solution of a Quadratic Equation

This Demonstration shows Lill's graphic method for solving a quadratic equation. The value is a root of the equation if and only if . In this case, the point is on a circle with diameter .
Special case: the golden ratio is the positive root of the equation .

### DETAILS

Here is a simple construction of the golden ratio. Draw a zigzag line through the points , , , . Let be a circle with radius and center at the midpoint of the segment . Let be the intersection of and an extension of .
The golden ratio is .
Reference
[1] D. Kurepa, Higher Algebra, Book 2 (in Croatian), Zagreb: Skolska knjiga, 1965 pp. 1072–1074.

### 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.