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mgf1107lecture24 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 24 Geometric Similarity Before discussing gnomons and how they relate to the Fibonacci sequence discussed last time, we need to revisit the concept of geometric similarity. While this is usually discussed in terms of triangles, it can be easily generalized to other figures. Triangles Two triangles are said to be similar if the corresponding angles are equal, and the corresponding sides have the same ratio. Squares Any two squares are similar, since Rectangles Two rectangles are similar if their corresponding sides have the same ratio.
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Circles and Disks Any two circles are similar. Any two disks are similar. Circular Rings Two circular disks are similar if both their inner and outer radii have the same ratio. Gnomons Definition: Given a geometric figure A, we say that a second figure G is a gnomon to A if it can be attached to A (with no overlap) in such a way that the resulting figure is similar to A.
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