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The altitudes of a triangle are the Cevians A_iH_i that are perpendicular to the legs A_jA_k opposite A_i. The three altitudes of any triangle are concurrent at the ...

The Bevan point V of a triangle DeltaABC is the circumcenter of the excentral triangle DeltaJ_AJ_BJ_C. It is named in honor of Benjamin Bevan, a relatively unknown Englishman ...

Given a set of n+1 control points P_0, P_1, ..., P_n, the corresponding Bézier curve (or Bernstein-Bézier curve) is given by C(t)=sum_(i=0)^nP_iB_(i,n)(t), where B_(i,n)(t) ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

A prime number p is called circular if it remains prime after any cyclic permutation of its digits. An example in base-10 is 1,193 because 1,931, 9,311, and 3,119 are all ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional ...

A tensor which has the same components in all rotated coordinate systems. All rank-0 tensors (scalars) are isotropic, but no rank-1 tensors (vectors) are. The unique rank-2 ...

The Johnson circumconic, a term used here for the first time, is the circumconic that passes through the vertices of both the reference triangle and the Johnson triangle. It ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...