The Pentagram: A Study

Topic:Angles, Cosine, Polygons, Pythagoras or Pythagorean Theorem, Trigonometry

1. Move the green points onto the red points to made a regular pentagon.

2. Move the green points onto the red points to make a pentagram.

3. Read the article in Britannica about the various ways cultures have used the pentagram as a symbol to represent different things at different times. Write in your own words one way that you have learned the shape of the pentagram has been used. Record any other sources you look up if you use information from them.

4. The turtle below is called Todd. Todd has been given some instructions of how to draw a pentagram. Click the buttons to instruct Todd to draw the star.

5. The interior angle of a regular pentagon is 108 degrees. Starting with the interior angle of the pentagon that is at the centre of the pentagram, create an argument to explain why the angle at each point of pentagram is 36 degrees. You can do so in words in the text box below or on the diagram below.

6. The radius of Todd's circle is 5 units. We can use this information to calculate that the length of one side of the star is 9.51 units (2 d.p.) Use the diagram below or the answer box below to show these calculations. Note, begin with the radius as 5 units, end with the length of one side of the star is 9.51 units.

7. Todd can either walk forward or turn counter clockwise. Give Todd instructions for drawing a pentagram. The angle Todd will turn is controlled on the slider. The distance Todd will walk is controlled by the number you put into the distance box. Click one of the buttons to issue an instruction to turn or to walk.

8. Take Todd for a walk. Todd can go anywhere but he must be within sight at all times and he must return to where he started.

The Pentagram: A Study

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