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Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. Examples of formulas include equations, equalities, identities, ...

The end of the last gap in the Lagrange spectrum, given by F=(2221564096+283748sqrt(462))/(491993569)=4.5278295661... (OEIS A118472). Real numbers greater than F are members ...

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

Let a spherical triangle have sides a, b, and c with A, B, and C the corresponding opposite angles. Then (sin[1/2(a-b)])/(sin(1/2c)) = (sin[1/2(A-B)])/(cos(1/2C)) (1) ...

The locus of a point P (or the envelope of a line) fixed in relation to a curve C which slides between fixed curves. For example, if C is a line segment and P a point on the ...

Two distinct knots cannot have the same exterior. Or, equivalently, a knot is completely determined by its knot exterior (Cipra 1988; Adams 1994, p. 261). The question was ...

The circumference of a graph is the length of any longest cycle in a graph. Hamiltonian graphs on n>1 vertices therefore have circumference of n. For a cyclic graph, the ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

Hackenbush is a game in combinatorial game theory in which player Left can delete any bLue edge, player Right can delete any Red edge, and either player can delete Green ...