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The "trefoil" curve is the name given by Cundy and Rollett (1989, p. 72) to the quartic plane curve given by the equation x^4+x^2y^2+y^4=x(x^2-y^2). (1) As such, it is a ...

Let a_1=1 and define a_(n+1) to be the least integer greater than a_n which cannot be written as the sum of at most h>=2 addends among the terms a_1, a_2, ..., a_n. This ...

The sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (OEIS A002024) consisting of 1 copy of 1, 2 copies of 2, 3 copies of 3, and so on. Surprisingly, there exist simple formulas ...

The evolute of the astroid is a hypocycloid evolute for n=4. Surprisingly, it is another astroid scaled by a factor n/(n-2)=4/2=2 and rotated 1/(2·4)=1/8 of a turn. For an ...

The involute of the astroid is a hypocycloid involute for n=4. Surprisingly, it is another astroid scaled by a factor (n-2)/n=2/4=1/2 and rotated 1/(2·4)=1/8 of a turn. For ...

The Paley class of a positive integer m=0 (mod 4) is defined as the set of all possible quadruples (k,e,q,n) where m=2^e(q^n+1), (1) q is an odd prime, and k={0 if q=0; 1 if ...

Proved in 1933. If q is an odd prime or q=0 and n is any positive integer, then there is a Hadamard matrix of order m=2^e(q^n+1), where e is any positive integer such that ...

A Steiner quadruple system is a Steiner system S(t=3,k=4,v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one ...

A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018). KP(3,3,1) is isomorphic to the 3-barbell graph. ...

Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its ...