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degrees. 360°. gradians. 400 g. The turn (symbol tr or pla) is a unit of plane angle measurement that is the angular measure subtended by a complete circle at its center. It is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) [1] or to one revolution (symbol rev or ...
For every fraction p / q (in its lowest terms) there is a Ford circle C[ p / q ], which is the circle with radius 1/(2q 2) and centre at ( p / q , 1 / 2q 2 ). Two Ford circles for different fractions are either disjoint or they are tangent to one another—two Ford circles never intersect.
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
Group operation. The set of rational points on the unit circle, shortened G in this article, forms an infinite abelian group under rotations. The identity element is the point (1, 0) = 1 + i 0 = 1. The group operation, or "product" is (x, y) * (t, u) = (xt − uy, xu + yt). This product is angle addition since x = cos (A) and y = sin (A), where ...
The Ford circle associated with the fraction / is denoted by [/] or [,]. There is a Ford circle associated with every rational number . In addition, the line y = 1 {\displaystyle y=1} is counted as a Ford circle – it can be thought of as the Ford circle associated with infinity , which is the case p = 1 , q = 0. {\displaystyle p=1,q=0.}
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser 's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = , giving the sequence 1, 2, 4 ...
where A is the area of an epicycloid with the smaller circle of radius r and the larger circle of radius kr (), assuming the initial point lies on the larger circle. A = ( − 1 ) k + 3 8 π a 2 {\displaystyle A={\frac {(-1)^{k}+3}{8}}\pi a^{2}}
Each of the purple squares has 1/4 of the area of the next larger square (1/2× 1/2 = 1/4, 1/4×1/4 = 1/16, etc.). The sum of the areas of the purple squares is one third of the area of the large square. Another geometric series (coefficient a = 4/9 and common ratio r = 1/9) shown as areas of purple squares.
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