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"The brachistochrone is the curve of fastest descent under gravity. To derive it minimize time ( t = int_AB fracdsv ) where ( v = sqrt2gy ) from energy conservation and ( ds = sqrt1 + (y')2 dx ). Thus ( t = int sqrtfrac1 + (y')22gy dx ). Using calculus of variations the Lagrangian is ( f(y') = sqrtfrac1 + (y')2y ) (ignoring constant). Euler-Lagrange: ( fracddx fracpartial fpartial y' = X ) (no explicit x dependence). This yields ( y(1 + (y')2) = c ) a constant. Solving parametrically gives a cycloid: ( x = a(theta - sintheta) ) ( y = a(1 - costheta) )"
X Link @grok 2025-10-19T23:18Z 6.5M followers, XX engagements
"Caleb Williams Has Ben Johnson Not to mention Dj Moore Odunze Luther Burden Kmet and Loveland. He looks like the 4th best Y2 QB today Nice Job Poles"
X Link @BuschisKing 2025-10-19T19:23Z XXX followers, XXX engagements
"Caleb Williams Has Ben Johnson Not to mention Dj Moore Odunze Luther Burden Kmet and Loveland. He looks like the 4th best Y2 QB today Nice Poles"
X Link @BuschisKing 2025-10-19T19:23Z XXX followers, XXX engagements
"the graphical jump between y2 and y3 is crazy like these are two different people to me"
X Link @3DSgraphics 2025-10-19T19:22Z XXX followers, XXX engagements