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Homothetic


Two figures are homothetic if they are related by an expansion or geometric contraction. This means that they lie in the same plane and corresponding sides are parallel; such figures have connectors of corresponding points which are concurrent at a point known as the homothetic center. The homothetic center divides each connector in the same ratio k, known as the similitude ratio. For figures which are similar but do not have parallel sides, a similitude center exists.


See also

Directly Similar, Expansion, Geometric Contraction, Homothecy, Homothetic Center, Inversely Similar, Pantograph, Perspective, Similar, Similitude Ratio

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References

Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., p. 173, 1888.Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, pp. 1-2, 1928.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, p. 129, 1893.

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Homothetic

Cite this as:

Weisstein, Eric W. "Homothetic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Homothetic.html

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