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This template shows a step by step illustration of the Euclidean algorithm. It is meant to illustrate the Euclidean algorithm article. This template depends on the Calculator gadget. If that gadget is not enabled, or js is not supported (e.g. when printing) the template is invisible.
This template shows a step by step illustration of the Euclidean algorithm. It is meant to illustrate the Euclidean algorithm article. This template depends on the Calculator gadget. If that gadget is not enabled, or js is not supported (e.g. when printing) the template is invisible.
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 ( theorems ) from these.
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147. Since ...
For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already constructed foci and major axis (think two pins and a piece of string) is just ...
Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. = + In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).
In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.
The British flag theorem can be generalized into a statement about (convex) isosceles trapezoids.More precisely for a trapezoid with parallel sides and and interior point the following equation holds: