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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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.
Informally we could say that G & A is similar to A.
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 Spring '08
 EVINSON
 Math, Calculus

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