Search results
Results from the WOW.Com Content Network
Thus a circle in the Euclidean plane was defined as the locus of a point that is at a given distance of a fixed point, the center of the circle. In modern mathematics, similar concepts are more frequently reformulated by describing shapes as sets; for instance, one says that the circle is the set of points that are at a given distance from the ...
A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle. Figure 4. The center N of the nine-point circle bisects a segment from the orthocenter H to the circumcenter O (making the orthocenter a center of dilation to both circles): [6]: p.152
An ellipse can be defined as the locus of points for which the sum of the distances to two given foci is constant. A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus.
The locus of points such that the sum of the squares of the distances to the given points is constant is a circle, whose centre is at the centroid of the given points. [22] A generalisation for higher powers of distances is obtained if, instead of n {\displaystyle n} points, the vertices of the regular polygon P n {\displaystyle P_{n}} are ...
Laguerre defined the power of a point P with respect to an algebraic curve of degree n to be the sum of the distances from the point to the intersections of a circle through the point with the curve, divided by the nth power of the diameter d. Laguerre showed that this number is independent of the diameter (Laguerre 1905).
Small circle of a sphere. In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius) from a given point on the sphere (the pole or spherical center).
The circle of equal altitude, also called circle of position (CoP), is defined as the locus of points on Earth on which an observer sees a celestial object such as the sun or a star, at a given time, with the same observed altitude.
An osculating circle Osculating circles of the Archimedean spiral, nested by the Tait–Kneser theorem. "The spiral itself is not drawn: we see it as the locus of points where the circles are especially close to each other." [1] An osculating circle is a circle that best approximates the curvature of a curve at a specific point.