Given 3 points : p1(x1,sin(x1)) p2(x2,sin(x2)) p3(x3,sin(x3)) does the following identity hold ?

if x2 < x3 and | x1 - x2 | < | x1 - x3| then distance(p1,p2) < distance(p1,p3)

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- Apr 22nd 2011, 11:16 AMErzenwaldPoints on a sine wave
Given 3 points : p1(x1,sin(x1)) p2(x2,sin(x2)) p3(x3,sin(x3)) does the following identity hold ?

if x2 < x3 and | x1 - x2 | < | x1 - x3| then distance(p1,p2) < distance(p1,p3) - Apr 22nd 2011, 11:19 AMMatt Westwood
Consider x_1 = 0, x_2 = pi/2, x_3 = pi.