Recall: A gnomon to a figure is a second shape that, when attached (with no overlap) to the original figure in the appropriate way, creates a new figure that is similar to the first figure.

Example: If we begin with the blue triangle shown below, we can create a new figure that is similar to the blue triangle by attaching the purple triangle shown. In this case, the purple triangle is gnomon to the blue triangle.

Note: The blue triangle is not gnomon to the purple triangle, as the resulting 2-colored triangle is not similar to the purple triangle.

Practice:

1. Draw or describe a figure that is gnomon to a rectangle of length 2 and width 1
2. Draw or describe a figure that is gnomon to a circle of radius 3.

Suppose ABC is any triangle with angles a , b, and c, and suppose that angle a is larger than angle b. Draw a gnomon to ABC which is also a triangle.

Do any rectangles have square gnomons? If so, which? That is, under what circumstances does a rectangle have a square gnomon?

Golden Ratio in Art, Revisited

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