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Given a source S and a curve gamma, pick a point on gamma and find its tangent T. Then the locus of reflections of S about tangents T is the orthotomic curve (also known as ...

The pedal coordinates of a point P with respect to the curve C and the pedal point O are the radial distance r from O to P and the perpendicular distance p from O to the line ...

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

A simple path is a path which is a simple curve. More precisely, a continuous mapping gamma:[a,b]->C^0 is a simple path if it has no self-intersections. Here, C^0 denotes the ...

A double point at which two (or more) osculating curves are tangent. The above plot shows the tacnode of the curve 2x^4-3x^2y+y^2-2y^3+y^4=0. The capricornoid and links curve ...

Pre-Calculus

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...