Comments on: e-day, or why cooking and math don’t mix http://threesixty360.wordpress.com/2008/02/06/e-day-or-why-cooking-and-math-dont-mix/ 12 tables, 24 chairs, and plenty of chalk Fri, 18 Dec 2009 14:06:39 +0000 http://wordpress.com/ hourly 1 By: Bacteria, Pancakes, and David X. Cohen « 360 http://threesixty360.wordpress.com/2008/02/06/e-day-or-why-cooking-and-math-dont-mix/#comment-979 Bacteria, Pancakes, and David X. Cohen « 360 Wed, 04 Jun 2008 00:00:47 +0000 http://threesixty360.wordpress.com/?p=198#comment-979 [...] world’s greatest cook they all came out to be different sizes. Further suppose that you got distracted while cooking and the pancakes came out burnt, but you piled them up anyway, in some random order. But then you [...] [...] world’s greatest cook they all came out to be different sizes. Further suppose that you got distracted while cooking and the pancakes came out burnt, but you piled them up anyway, in some random order. But then you [...]

]]> By: Alon Levy http://threesixty360.wordpress.com/2008/02/06/e-day-or-why-cooking-and-math-dont-mix/#comment-308 Alon Levy Fri, 08 Feb 2008 01:31:06 +0000 http://threesixty360.wordpress.com/?p=198#comment-308 Actually, there are only finitely many solutions to b^3 = 2c^2 - 1, by Siegel's theorem on integer points on elliptic curves. In general, any equation in two variables of degree higher than two that satisfies certain smoothness conditions will have finitely many integer solutions. Actually, there are only finitely many solutions to b^3 = 2c^2 – 1, by Siegel’s theorem on integer points on elliptic curves. In general, any equation in two variables of degree higher than two that satisfies certain smoothness conditions will have finitely many integer solutions.

]]> By: TwoPi http://threesixty360.wordpress.com/2008/02/06/e-day-or-why-cooking-and-math-dont-mix/#comment-299 TwoPi Thu, 07 Feb 2008 13:45:41 +0000 http://threesixty360.wordpress.com/?p=198#comment-299 Indeed, any individual solution will lead to an infinite family of solutions by scaling (multiply both sides of the equation by any perfect 12th power...). I've done some numerical experiments with different values of $latex c^2 - a$, but have yet to see patterns or generate conjectures. Poking around Sloane's On-line Encyclopedia of Integer Sequences for related sequences (values of $latex c^2 - a$ where solutions exist, or of <i>c</i>, or etc.) came up empty. Dickson's <i>History of the Theory of Numbers</i> mentioned one related result involving triangular numbers, but I want to track down the source before commenting further on that. (And Dickson's <i>History...</i> is huge -- I'm not confident that I didn't miss something else there.) Indeed, any individual solution will lead to an infinite family of solutions by scaling (multiply both sides of the equation by any perfect 12th power…).

I’ve done some numerical experiments with different values of c^2 - a, but have yet to see patterns or generate conjectures.

Poking around Sloane’s On-line Encyclopedia of Integer Sequences for related sequences (values of c^2 - a where solutions exist, or of c, or etc.) came up empty.

Dickson’s History of the Theory of Numbers mentioned one related result involving triangular numbers, but I want to track down the source before commenting further on that. (And Dickson’s History… is huge — I’m not confident that I didn’t miss something else there.)

]]>