# The Diagonal Paradox

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Consider the stepped line . As goes to infinity, approaches the hypotenuse of the isosceles right triangle that has length . So the length of the limit of is . Is this right?

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Contributed by: Izidor Hafner (January 2016)

Open content licensed under CC BY-NC-SA

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Reference

[1] E. P. Northrop, *Riddles in Mathematics, A Book of Paradoxes*, Mineola, NY: Dover Publications, Inc., 2014 pp. 138–139.

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