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Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

The nested radical constant is the constant defined by C = sqrt(1+sqrt(2+sqrt(3+sqrt(4+sqrt(5+...))))) (1) = 1.75793275... (2) (OEIS A072449). No closed-form expression is ...

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

The functions theta_s(u) = (H(u))/(H^'(0)) (1) theta_d(u) = (Theta(u+K))/(Theta(k)) (2) theta_c(u) = (H(u))/(H(K)) (3) theta_n(u) = (Theta(u))/(Theta(0)), (4) where H(u) and ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

A noble number nu is defined as an irrational number having a continued fraction that becomes an infinite sequence of 1s at some point, nu=[0,a_1,a_2,...,a_n,1^_]. The ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

A graphical plot which can be used for solving certain types of equations. According to Steinhaus (1999, p. 301), the Nomogram was invented by the French mathematicians ...

The noncentral chi-squared distribution with noncentrality parameter lambda is given by P_r(x) = ...

A proof which indirectly shows a mathematical object exists without providing a specific example or algorithm for producing an example. Nonconstructive proofs are also called ...