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The fixed point with respect to which a pedal curve or pedal triangle is drawn.

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...

The evolute of the prolate cycloid x = at-bsint (1) y = a-bcost (2) (with b>a) is given by x = a[t+((bcost-a)sint)/(acost-b)] (3) y = (a(a-bcost)^2)/(b(acost-b)). (4)

Let t, u, and v be the lengths of the tangents to a circle C from the vertices of a triangle with sides of lengths a, b, and c. Then the condition that C is tangent to the ...

The catacaustic of the quadrifolium with arbitrary radiant point is a complicated function. A few example are illustrated above.

The Scarabaeus curve is a sextic curve given by the equation (x^2+y^2)(x^2+y^2+ax)^2-b^2(x^2-y^2)^2=0 and by the polar equation r=bcos(2theta)-acostheta where a,b!=0.

If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...