Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
Bernoulli's lightray solution for the brachistochrone problem from ...
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Arclength cycloidarclengths = s(ϕ) (using Pythagoras):ds = √ dx 2 +dy 2 == √ (dx/dϕ) 2 +(dy/dϕ) 2 dϕ == ̺√2 √ 1+cosϕ dϕ = 2̺cos ϕ 2 dϕ s(ϕ) = 4̺sin ϕ 2