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Two triangles are similar if their triples of vertex angles are the same.

A system is singular if its condition number is infinite and ill-conditioned if it is too large.

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 ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

The dual polyhedron of the small icosihemidodecahedron U_(49) and Wenninger dual W_(89). When rendered, the small icosihemidodecacron and small dodecahemidodecacron appear ...

The dual polyhedron of the truncated great dodecahedron U_(37) and Wenninger dual W_(75).

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

A 4-multiperfect number P_4. 36 sous-triples are known (30240, 32760, 2178540, 23569920, ...; OEIS A027687), and these are believed to comprise all sous-triples.