Diophantine imaging reveals the broken symmetry of sums of integer cubes
Diophantine imaging reveals the broken symmetry of sums of integer cubes
Abstract We introduced a novel method for visualizing large diophantine datasets and in particular found that mapping the known integer triplets $$\{a,b,c\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> solving either equations of the type $$a^3+b^3+c^3=d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>a</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> …