Circles whose tangent lines at the points of intersection are perpendicular
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Three mutually orthogonal circles
In geometry, two circles are said to be orthogonal if their respective tangent lines at the points of intersection are perpendicular (meet at a right angle).
A 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 geometry, then an orthogonal pair of lines or line and circle are orthogonal generalized circles.
In the conformal disk model of the hyperbolic plane, every geodesic is an arc of a generalized circle orthogonal to the circle of ideal points bounding the disk.
and 26 Related for: Orthogonal circles information
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...
intersect two given circlesorthogonally, can be extended to the construction of two orthogonally intersecting systems of circles: Let c 1 , c 2 {\displaystyle...
mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, laureate...
circle at a point P is perpendicular to the radius to that point, theorems involving tangent lines often involve radial lines and orthogonalcircles....
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...
mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the...
pencil of concentric circles are the lines through their common center (see diagram). Suitable methods for the determination of orthogonal trajectories are...
mutually orthogonalcircles. The first family consists of the circles with all possible distance ratios to two fixed foci (the same circles as in #1)...
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...
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...
In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...
to six great circles, which correspond to mirror planes in tetrahedral symmetry. They can be grouped into three pairs of orthogonalcircles (which typically...
mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other...
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 geometry, Villarceau circles (/viːlɑːrˈsoʊ/) are a pair of circles produced by cutting a torus obliquely through its center at a special angle. Given...
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...
Bipolar coordinates are a two-dimensional orthogonal coordinate system based on the Apollonian circles. Confusingly, the same term is also sometimes used...
parabolas which intersect orthogonally (see below). A circle is an ellipse with both foci coinciding at the center. Circles that share the same focus...
many circles (and hyperbolas) twisting around one another. At each point in a N-dimensional Lie group there can be N different orthogonalcircles, tangent...
In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity...
In mathematics, orthogonal coordinates are defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots...
is isomorphic with the orthogonal group O(2). A 2-dimensional object with circular symmetry would consist of concentric circles and annular domains. Rotational...
instance of the more general mathematical concept of orthogonality; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced...
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...
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