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The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
Hence, given the radius, r, center, P c, a point on the circle, P 0 and a unit normal of the plane containing the circle, ^, one parametric equation of the circle starting from the point P 0 and proceeding in a positively oriented (i.e., right-handed) sense about ^ is the following:
The center of all rectangular hyperbolas that pass through the vertices of a triangle lies on its nine-point circle. Examples include the well-known rectangular hyperbolas of Keipert, Jeřábek and Feuerbach. This fact is known as the Feuerbach conic theorem. The nine point circle and the 16 tangent circles of the orthocentric system
where a is the radius of the circle, (,) are the polar coordinates of a generic point on the circle, and (,) are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of ...
The general equation for a circle with a center at (,) and radius a is + =. This can be simplified in various ways, to conform to more specific cases, such as the equation r ( φ ) = a {\displaystyle r(\varphi )=a} for a circle with a center at the pole and radius a .
A circle is drawn centered on the midpoint of the line segment OP, having diameter OP, where O is again the center of the circle C. The intersection points T 1 and T 2 of the circle C and the new circle are the tangent points for lines passing through P, by the following argument.
The circle with center at Q and with radius R is called the osculating circle to the curve γ at the point P. If C is a regular space curve then the osculating circle is defined in a similar way, using the principal normal vector N. It lies in the osculating plane, the plane spanned by the tangent and principal normal vectors T and N at the ...
These points are located at the intersection of the circle with the vertical line passing through the center of the circle, . Thus, the magnitude of the maximum and minimum shear stresses are equal to the value of the circle's radius R {\displaystyle R}