The Golden Ratio

Composition with Gray and Light Brown
by Piet Mondrian
1918 (170 Kb);
Oil on canvas, 80.2 x 49.9 cm;
Museum of Fine Arts, Houston, Texas

The above picture has many, many rectangles. Let's explore the ratio of lenth to width for various rectangles. Start by choosing your favorite rectangle, either from the picure above, or draw one for yourself. Measure the length. Measure the width. Find the ratio of length to width.

Fold your left index finger in on itself. The knuckle on your hand to the middle knuckle form the length of a rectangle, and between the middle and top knuckle the width of the rectangle is formed.

What is the ratio for a 3" X 5" card? How about a sheet of notebook paper? Record your results in the table below.

rectangle length width ratio of length to width
my favorite ______ ______ ______________
3" x 5" index card ______ ______ ______________
8.5" X 11" paper ______ ______ ______________
2" X 3" school photo ______ ______ ______________
finger rectangle ______ ______ ______________
another rectangle ______ ______ ______________
and another ______ ______ ______________
and another ______ ______ ______________
just one more? ______ ______ ______________

What do you notice about these ratios? Take the average of all the ratios you find.
Is the number you get close to this

Chances are that it is. You will see that this has been a special number for hundreds of years.

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