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geom3d[homothety] - Find the homothety of a geometric object
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Calling Sequence
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homothety(Q, P, k, O)
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Parameters
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Q
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the name of the object to be created
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P
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geometric object
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k
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number which is the ratio of the homothety
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O
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point which is the center of the homothety
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Description
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In homothety, each point P of the set S of all points of unextended space is carried into the point P1 of S collinear with P and a fixed point O of space, and such that  , where k is a nonzero real number. Note that OP1, OP denote the sensed magnitudes of OP1 and OP.
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For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
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The command with(geom3d,homothety) allows the use of the abbreviated form of this command.
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Examples
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Define an icosahedron with center (0,0,0), radius of the circum-sphere 1
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Construct a stellate (#10 in this example) of the given icosahedron
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Apply homothety transformation to p2 with ratio 3, and o being the center of the homothety
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Plotting:
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![draw([p2, p3], scaling = constrained, style = patch, lightmodel = light4, orientation = [0, 32], title = `homothety of a stellated icosahedron`)](/support/helpjp/helpview.aspx?si=5967/file04010/math138.png)
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Download Help Document
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