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:
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