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The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

The problem of polygon intersection seeks to determine if two polygons intersect and, if so, possibly determine their intersection. For example, the intersection of the two ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

Inscribe two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 in a reference triangle DeltaABC such that A = ∠AB_1C_1=∠AC_2B_2 (1) B = ∠BC_1A_1=∠BA_2C_2 (2) C = ∠CA_1B_1=∠CB_2A_2. ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...