Divide the interval [ a , b ] into n equal segments with endpoints t 0 = a , t 1 , t 2 , … … , t n = b and let Δ Δ t = t k − − t k − − 1 . Rather than a smooth function y ( t ) we consider the polygonal line with vertices ( t 0 , y 0 ) , … … , ( t n , y n ) , where y 0 = A and y n = B . Accordingly, our functional becomes a real function of n − − 1 variables given by J ( y 1 , … … , y n − − 1 ) ≈ ≈ ∑ ∑ k = 0 n − − 1 L ( t k , y k , y k + 1 − − y k Δ Δ t ) Δ Δ t .