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Hidden length!

Consider the sequence of triangles: See Figure.

\Huge {Animated figure
to be inserted here}

Notice that the length of each curve in the sequence is constant and equal to $\sqrt{2} $, but they become arbitrary close to the straight segment $[0,1]$. The limiting object is the segment $[0,1]$ but its length is still equal to $\sqrt{2} $.

Andre Cherkaev