straight line through a circle's center is orthogonal to it, and if straight lines are also considered as a kind of generalized circles, for instance in inversive...

intersecting circles is the common secant of two convenient equipower circles (see below Orthogonal cicles). For a point P {\displaystyle P} outside a circle c i...

circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonal circles....

Determination of a circle, that intersects four circles by the same angle. Solving the Problem of Apollonius Construction of the Malfatti circles: For a given...

Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and...

mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate...

mutually orthogonal circles. The first family consists of the circles with all possible distance ratios to two fixed foci (the same circles as in #1)...

pencil of concentric circles are the lines through their common center (see diagram). Suitable methods for the determination of orthogonal trajectories are...

tangent circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to...

of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally; the construction...

symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. All circles are similar. A circle circumference and radius...

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the...

many circles (and hyperbolas) twisting around one another. At each point in a N-dimensional Lie group there can be N different orthogonal circles, tangent...

Homographies of the complex plane preserve orthogonal circles...

In geometry, Villarceau circles (/viːlɑːrˈsoʊ/) are a pair of circles produced by cutting a torus obliquely through its center at a special angle. Given...

circles is orthogonal to every circle in the pencil they determine. The circles orthogonal to two fixed circles form a pencil of circles. Two circles...

inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves...

is the circumference, or length, of any one of its great circles. The circumference of a circle is the distance around it, but if, as in many elementary...

Bipolar coordinates are a two-dimensional orthogonal coordinate system based on the Apollonian circles. There is also a third system, based on two poles...

The circle group is isomorphic to the special orthogonal group ⁠ S O ( 2 ) {\displaystyle \mathrm {SO} (2)} ⁠. One way to think about the circle group...

parabolas which intersect orthogonally (see below). A circle is an ellipse with both foci coinciding at the center. Circles that share the same focus...

separation between various types and orders of aberrations. Zernike's orthogonal circle polynomials provided a solution to the long-standing problem of the...

square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford...

mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...

horizontal circles (red). The purple planes intersect at vertical circles (green). The curvature lines of a torus generate a net of orthogonal circles. A torus...

curvature of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most...

any reference to circles in the definition of π, so that statements about the relation of π to the circumference and area of circles are actually theorems...

and β as they cross. If a circle γ crosses circles α and β at equal angles, then γ is crossed orthogonally by one of the circles of antisimilitude of α and...