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A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter.
The circle is the closed curve of least perimeter that encloses the maximum area. This is known as the isoperimetric inequality, which states that if a rectifiable Jordan curve in the Euclidean plane has perimeter C and encloses an area A (by the Jordan curve theorem) then.
v. t. e. In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. [1] The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [2] More generally, the perimeter is the curve length around any closed figure.
The circles of Apollonius of a triangle are three circles, each of which passes through one vertex of the triangle and maintains a constant ratio of distances to the other two. The isodynamic points and Lemoine line of a triangle can be solved using these circles of Apollonius. Apollonius' problem is to construct circles that are simultaneously ...
A circle viewed from a side angle looks like an ellipse: that is, the ellipse is the image of a circle under parallel or perspective projection. The ellipse is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency: a similar effect leads to elliptical polarization of light in ...
Incircle and excircles. Incircle and excircles of a triangle. In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2 ...
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two- dimensional surface of a sphere [a] or the n -dimensional surface of higher dimensional spheres. Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry ...