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y^m=kx^n(a-x)^b. The curves with integer n, b, and m were studied by de Sluze between 1657 and 1698. The name "Pearls of Sluze" was given to these curves by Blaise Pascal ...

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 ...