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This equation, known as the equation of the circle, ... plane can be broken into two semicircles each of which is the graph of a function, ...
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation + =. In general, every implicit curve is defined by an equation of the form (,) =
The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes , whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra and calculus .
For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
(The generator circle is the inverse curve of the parabola's directrix.) This property gives rise to the following simple method to draw a cardioid: Choose a circle and a point on its perimeter, draw circles containing with centers on , and; draw the envelope of these circles.
These equations for the Mohr circles show that all admissible stress points (,) lie on these circles or within the shaded area enclosed by them (see Figure 10). Stress points ( σ n , τ n ) {\displaystyle (\sigma _{\mathrm {n} },\tau _{\mathrm {n} })} satisfying the equation for circle C 1 {\displaystyle C_{1}} lie on, or outside circle C 1 ...