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  2. Go and mathematics - Wikipedia

    en.wikipedia.org/wiki/Go_and_mathematics

    Without ko, Go is PSPACE-hard. [2] This is proved by reducing True Quantified Boolean Formula, which is known to be PSPACE-complete, to generalized geography, to planar generalized geography, to planar generalized geography with maximum degree 3, finally to Go positions. Go with superko is not known to be in PSPACE.

  3. Principia Mathematica - Wikipedia

    en.wikipedia.org/wiki/Principia_Mathematica

    The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.

  4. Doubling the cube - Wikipedia

    en.wikipedia.org/wiki/Doubling_the_cube

    In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 1 3 = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.

  5. Square–cube law - Wikipedia

    en.wikipedia.org/wiki/Square–cube_law

    Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.

  6. Graduate Studies in Mathematics - Wikipedia

    en.wikipedia.org/wiki/Graduate_Studies_in...

    Volume I: Elementary Theory, Richard V. Kadison, John R. Ringrose (1997, ISBN 978-0-8218-0819-1) [2] 16 Fundamentals of the Theory of Operator Algebras. Volume II: Advanced Theory, Richard V. Kadison, John R. Ringrose (1997, ISBN 978-0-8218-0820-7) [3] 17 Topics in Classical Automorphic Forms, Henryk Iwaniec (1997, ISBN 978-0-8218-0777-4)

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