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A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...

The tribox, also called the Penrose rectangle or Penrose square, is an impossible figure that is the generalization of the Penrose triangle from a triangle to a square. ...

Let F_n be the nth Fibonacci number, and let (p|5) be a Legendre symbol so that e_p=(p/5)={1 for p=1,4 (mod 5); -1 for p=2,3 (mod 5). (1) A prime p is called a Wall-Sun-Sun ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...

If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice. Renteln ...

Several prizes are awarded periodically for outstanding mathematical achievement. There is no Nobel Prize in mathematics, and the most prestigious mathematical award is known ...

A special function is a function (usually named after an early investigator of its properties) having a particular use in mathematical physics or some other branch of ...

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...