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In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer d such that the imaginary quadratic field [] has class number 1. Equivalently, the ring of algebraic integers of Q [ − d ] {\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has unique factorization .
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 .
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
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
A Assuming an altitude of 194 metres above mean sea level (the worldwide median altitude of human habitation), an indoor temperature of 23 °C, a dewpoint of 9 °C (40.85% relative humidity), and 760 mmHg sea level–corrected barometric pressure (molar water vapor content = 1.16%). B Calculated values *Derived data by calculation.
Any old scientific calculator would disprove your method in seconds, but you failed to check. Why? We are looking for a numeric result of the order 2.6x10^17, and Pi^root163 is of the order 2,224,255, and e^222 is of the order 2.6x10^96 already. Clearly a drastic mistake! [Though a^(b×c) works.]