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The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures (for example, when the side of a square or the radius of a circle is multiplied by three, its area is multiplied by nine — i.e. by three squared). The altitudes of similar triangles are in the same ratio as ...
The solution in which the three rectangles are all of different sizes and where they have aspect ratio ρ 2, where ρ is the plastic ratio. The fact that a rectangle of aspect ratio ρ 2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ρ 2 related to the Routh–Hurwitz ...
Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-line velocity) and the same Reynolds and Womersley numbers, then the fluid flows will be identical.
Golden spirals are self-similar. The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
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.
Two triangles are said to be similar, if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity. [39] Some basic theorems about similar triangles are:
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