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The second Morley cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=1, 1134, 1135, 1136, and 1137.

Given an ideal A, a semiprime ring is one for which A^n=0 implies A=0 for any positive n. Every prime ring is semiprime.

A phase curve (i.e., an invariant manifold) which meets a hyperbolic fixed point (i.e., an intersection of a stable and an unstable invariant manifold) or connects the ...

The pedal curve of a sinusoidal spiral r=a[cos(nt)]^(1/n) with pedal point at the center is another sinusoidal spiral with polar equation r=a[cos(nt)]^(1+1/n). A few examples ...

The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

The stirrup curve is the quartic curve given by the equation (x^2-1)^2=y^2(y-1)(y-2)(y+5).

A subspace A of X is called a strong deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X, a in A, and t in I, 1. F(x,0)=x, 2. ...

Let (x_0,y_0) be any point of a surface function z=f(x,y). Then the surface has a nonvertical tangent plane at (x_0,y_0) with equation ...