Discovering with Geometer's Sketchpad

LESSON 2

• What do the angles in a five pointed star drawn inside a circle add up to?
  
• Have a guess... then use Geometer's Sketchpad to test your conjecture.

• What about the angles in the polygon at the centre of the the star?
  
• What about stars with different numbers of points?

Write up your findings using the computer then make a print out for your notes. Use helpful diagrams so that someone else can understand what you have found out.

• Adjust the five pointed star so that all the five angles are the same. You have made a Pentagram, a shape which was used by the Pythagorean society (2500 years ago) as a secret sign. It has interesting mathematical properties and was said by some to have magical powers.
  One of the properties of this shape is that the the lengths of some of the line segments are in the golden ratio.
  Find out about the golden ratio and show how it relates to the pentagram.
  
• Use Geometer's Sketchpad to design your own secret sign. Your shape should have interesting mathematical properties too.

Getting "Geometer's Sketchpad"