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Roger Penrose's solution of the illumination problem using elliptical arcs (blue) and straight line segments (green), with 3 positions of the single light source (red spot). The purple crosses are the foci of the larger arcs. Lit and unlit regions are shown in yellow and grey respectively.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
Starlight overcast moonless night sky [1] 140 microlux: Venus at brightest [1] 200 microlux: Starlight clear moonless night sky excluding airglow [1] 10 −3: 1 millilux: 2 millilux: Starlight clear moonless night sky including airglow [1] 10 −2: 1 centilux: 1 centilux: Quarter Moon 10 −1: 1 decilux: 2.5 decilux: Full Moon on a clear night ...
A common and simple version of this problem asks to measure a time of 45 seconds using only two fuses that each burn for a minute. The assumptions of the problem are usually specified in a way that prevents measuring out 3/4 of the length of one fuse and burning it end-to-end, for instance by stating that the fuses burn unevenly along their length.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...