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Ramanujan's constant is the transcendental number [5], which is an almost integer: [6] = … +. This number was discovered in 1859 by the mathematician Charles Hermite. [7] In a 1975 April Fool article in Scientific American magazine, [8] "Mathematical Games" columnist Martin Gardner made the hoax claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa ...
Heegner points are special points on elliptic curves The Stark–Heegner theorem identifies the imaginary quadratic fields of class number 1. A Heegner number is a number n such that Q ( √ − n ) is an imaginary quadratic field of class number 1.
In number theory, the Heegner theorem [1] establishes the complete list of the quadratic imaginary number fields whose rings of integers are principal ideal domains. It solves a special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed class number .
The number e π √ 163 is known as Ramanujan's constant. Its decimal expansion is given by: e π √ 163 = 262 537 412 640 768 743.999 999 999 999 250 072 59... (sequence A060295 in the OEIS) which suprisingly turns out to be very close to the integer 640320 3 + 744: This is an application of Heegner numbers, where 163 is the
Kurt Heegner (German: [ˈheːɡnɐ]; 16 December 1893 – 2 February 1965) was a German private scholar from Berlin, who specialized in radio engineering and mathematics. He is famous for his mathematical discoveries in number theory and, in particular, the Stark–Heegner theorem .
Ed Pegg Jr. noted that the length d equals (), which is very close to 7 (7.0000000857 ca.) [1] In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one.
The phenomenon is related to the Ulam spiral, which is also implicitly quadratic, and the class number; this polynomial is related to the Heegner number =. There are analogous polynomials for p = 2 , 3 , 5 , 11 and 17 {\displaystyle p=2,3,5,11{\text{ and }}17} (the lucky numbers of Euler ), corresponding to other Heegner numbers.
In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. They were defined by Bryan Birch and named after Kurt Heegner , who used similar ideas to prove Gauss's conjecture on imaginary quadratic fields of class number one.