Investigating Mathematics with GeoGebra

Henrico County Public Schools

Construction of the Golden Section

READ the instructions on the right and INTERACT with the GeoGebra applet below.
Click on the reset icon icon to reset the diagram.

Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.

Investigation Steps

Follow the directions to create the construction below.
GoldenMeanConstruction

 Step 1 Close 
  1. Use the Segment between two points tool to create a line segment.
  2. Use the Midpoint tool to find midpoint of AB.
  3. Use the Angle with given size tool to create a clockwise angle (90°) from the midpoint to point B.
  4. Use the Segment between two points tool to create segments AD and BD.
 Step 2 Close 
  1. Use Circle with center through point tool and create a circle with center D and raduis B.
  2. Mark the Intersection of the circle and line segment AD.
  3. Create a circle with center A and raduis E.
  4. Mark the Intersection of segment AB and the circle.
 Step 3 Close 
  1. Create segments AF and FB.
  2. Use the Distance tool and click on segment AF and FB.
  3. Use the Text tool to enter " GOLDEN RATIO = " + f/g.

  4. Move points A and B, what do you notice about the RATIO?