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Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

A curve whose name means "shell form." Let C be a curve and O a fixed point. Let P and P^' be points on a line from O to C meeting it at Q, where P^'Q=QP=k, with k a given ...

A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume ...

Given the above figure (without looking at the figure below!), determine how to disengage the two slotted cube halves without cutting, breaking, or distorting. One possible ...

The Curry triangle, also sometimes called the missing square puzzle, is a dissection fallacy created by American neuropsychiatrist L. Vosburgh Lions as an example of a ...

The operation of drilling a tubular neighborhood of a knot K in S^3 and then gluing in a solid torus so that its meridian curve goes to a (p,q)-curve on the torus boundary of ...

The number 2^(1/3)=RadicalBox[2, 3] (the cube root of 2) which is to be constructed in the cube duplication problem. This number is not a Euclidean number although it is an ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...