Activity 9: The Golden Section

Sometimes the Golden Ratio that you discovered on the last Activity is known as the Golden Section. This is because it describes a special ratio in which a line can be divided.

It still equals approximately 1.62.

This ratio can be found in places other than in Golden Rectangles. Here is one.

Draw a regular pentagon.

It can be made from three isosceles triangles.



Draw in the rest of the diagonals.

What type of shape is VWXYZ?

Look at the diagonal EB. Measure EW and WB. Divide EW by WB.
Now measure EB and EW. Divide EB by EW.

What do you get in each case?

Try other diagonals or bits of diagonals.

Are any of the sides of the isosceles triangles in the Golden Ratio? If so, which?

Make a list of those whose ratios are approximately 1.62.

These lines are said to be divided in the Golden Section.