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Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, ISBN 978-1-56881-220-5 (Orbifold notation for polyhedra, Euclidean and hyperbolic tilings) On Quaternions and Octonions , 2003, John Horton Conway and Derek A. Smith ISBN 978-1-56881-134-5
In mathematics, the Euclidean algorithm, [note 1] or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (c. 300 BC).
A spiral similarity taking triangle ABC to triangle A'B'C'. Spiral similarity is a plane transformation in mathematics composed of a rotation and a dilation. [1] It is used widely in Euclidean geometry to facilitate the proofs of many theorems and other results in geometry, especially in mathematical competitions and olympiads.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions from these.
A Euclidean isometry can be direct or indirect, depending on whether it preserves the handedness of figures. The direct Euclidean isometries form a subgroup, the special Euclidean group, often denoted SE(n) and E + (n), whose elements are called rigid motions or Euclidean motions. They comprise arbitrary combinations of translations and ...
Figure 6: Euclidean genetic distance between 51 worldwide human populations, calculated using 289,160 SNPs. [30] Dark red is the most similar pair and dark blue is the most distant pair. Euclidean distance is a formula brought about from Euclid's Elements, a 13 book set detailing the foundation of all euclidean mathematics.
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