The ABC conjecture [La conjecture ABC].
The horizontal and vertical axes display respectively the integer numbers from 1 to N.
Each disk display a couple of coprime numbers A (X axis) and B (Y axis):
The number C is the sum of A and B:
C = A+B
The function Radical(N) gives the product of the prime factors (with an exponent equals to 1) of N.
N = 1960 = 23x51x72
Radical(1960) = 21x51x71 = 2x5x7 = 70
Then the following function is computed:
k(A,B,C) = ---------------------
The ABC conjecture states that k(A,B,C) is less than a certain constant (unknown, but greater than 1 and
hopefully lesser than 2...) whatever the values of A and B.
The surface and the luminance of each disk are proportional to k(A,B,C).
For this picture, the numbers A and B belong to [1,N=20]
giving birth to the following values:
See some tridimensional visualizations:
See some related pictures (including this one):
(CMAP28 WWW site: this page was created on 09/26/2012 and last updated on 09/06/2022 10:57:54 -CEST-)
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