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THE SHORTEST DISTANCE BETWEEN 2 POINTS IS A STRAIGHT LINE… Packers Nation… Chris McClellan is a GROWN ASS MAN, who creates his own straight lines!!! #GoPackGo
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![What Curve Beats a Straight Line? Take two fixed points A and B. A bead slides without friction under gravity. Among all possible curves connecting A to B, which one gives the smallest travel time? This is the Brachistochrone problem. The time functional is T[y] = ∫ √((1 + y′²)/(2gy)) dx where y is the vertical drop from the starting point. The winning curve is not a straight line. It is a cycloid x(θ) = a(θ - sin θ) y(θ) = a(1 - cos θ) The bead first falls steeply to gain speed, then uses that speed across the remaining distance. The path is longer than the straight segment, yet the travel time is smaller. The shortest path solves geometry. The fastest path solves variation. #CalculusOfVariations #Brachistochrone #Cycloid #ClassicalMechanics #MathematicalPhysics #Optimization #DifferentialEquations #PhysicsAnimation #Mathematics](https://image.24vids.com/tw-2070226540810428705/amplify_video_thumb/2070226188677644288/img/-_2rUKA6DxvJw6EX.jpg)
