Point from which two similar geometric figures can be scaled to each other
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Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center.
In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another. If the center is external, the two figures are directly similar to one another; their angles have the same rotational sense. If the center is internal, the two figures are scaled mirror images of one another; their angles have the opposite sense.
Figure 2: Two geometric figures related by an external homothetic center S. The angles at corresponding points are the same and have the same sense; for example, the angles ∠ABC, ∠A'B'C' are both clockwise and equal in magnitude.
In geometry, a homotheticcenter (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar...
dilation HomotheticcenterHomothetic vector field Homothetic preferences This disambiguation page lists articles associated with the title Homothetic. If...
homotheticcenter, whereas the internal tangent lines intersect at the internal homotheticcenter. Both the external and internal homotheticcenters lie...
exceeds 1. The above-mentioned fixed point S is called homotheticcenter or center of similarity or center of similitude. The term, coined by French mathematician...
It is equivalent to a homothetic transformation with scale factor −1. The point of inversion is also called homotheticcenter. An object that is invariant...
orthocentric system is always homothetic to the original system of four points with the common nine-point center as the homotheticcenter and α the ratio of similitude...
points: the radical center G of the three given circles and the pole in C1 of one of the four lines connecting the homotheticcenters. Finding the same...
of P is homothetic to the antipedal triangle of P −1. The homotheticcenter (which is a triangle center if and only if P is a triangle center) is the...
the Johnson triangle. The homotheticcenter of the Johnson triangle and the reference triangle is their common nine-point center. Property 1 is obvious from...
through both Soddy centers, called the Soddy line, also passes through the incenter of the triangle, which is the homotheticcenter of the two Soddy circles...
the circumradius of the triangle; the de Longchamps point is the homotheticcenter of the Steiner circle and the circumcircle. As the reflection of the...
excircles. These two triangles are similar and the Clawson point is their center of similarity, therefore the three lines TAHA, TBHB, TCHC connecting their...
the lines AHAO, BHBO, CHCO and triangle ABC are homothetic and congruent, and the homotheticcenter lies on the line OH. If OH is any line through the...
perfect competitor in all input markets) and the production function is homothetic, a firm experiencing constant returns will have constant long-run average...
convex body C in the plane, we can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C and the positive homothety ratio...
∺ ∺ U+223A HTML 5.0 geometric proportion ∻ ∻ U+223B HTML 5.0 homothetic ∼ ∼ ∼ ∼ ∼ U+223C HTML 4.0 HTML 5.0 HTML 5.0...
points if the pedal triangle of P is homothetic to the antipedal triangle of Q and the pedal triangle of Q is homothetic to the antipedal triangle of P. Given...
structure on individuals. Extreme case: two groups of variables that define homothetic clouds of individuals N i j {\displaystyle N_{i}^{j}} coincide. The coordinate...
combination of two inversions in concentric circles results in a similarity, homothetic transformation, or dilation characterized by the ratio of the circle radii...
the reference triangle).: p. 447 : p. 102 The tangential triangle is homothetic to the orthic triangle.: p. 98 A reference triangle and its tangential...
interval on a ray is given by logarithmic measure so it is invariant under a homothetic transformation ( x , y ) ↦ ( λ x , λ y ) , λ > 0. {\displaystyle (x,y)\mapsto...
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