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The parametric equations of the evolute of an epitrochoid specified by circle radii a and b with offset h are x = ...

The gear curve is a curve resembling a gear with n teeth given by the parametric equations x = rcost (1) y = rsint, (2) where r=a+1/btanh[bsin(nt)], (3) where tanhx is the ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

The evolute of a hyperbola with parametric equations x = acosht (1) y = bsinht (2) is x_e = ((a^2+b^2))/acosh^3t (3) y_e = -((a^2+b^2))/bsinh^3t, (4) which is similar to a ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

For x(0)=a, x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)]. (2) If a/b=n, then x = 1/(n-2)[(n-1)cosphi-cos[(n-1)phi]a (3) y = ...

The hypocycloid x = a/(a-2b)[(a-b)cosphi-bcos((a-b)/bphi)] (1) y = a/(a-2b)[(a-b)sinphi+bsin((a-b)/bphi)] (2) has involute x = (a-2b)/a[(a-b)cosphi+bcos((a-b)/bphi)] (3) y = ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.