Shirali, Shailesh
(2019)
A counterintuitive Pythagorean surprise.
At Right Angles (4).
pp. 1921.
ISSN 25821873
Abstract
The following is sometimes presented as a phenomenon in mathematics that goes counter to our intuition. Imagine a tightly stretched rope from one end of a field to another, tied down at its ends. For simplicity, we take the length of the field to be 100 m; so the length of the rope is 100 m. Now replace this rope by one that is slightly longer, say by 20 cm. There is some slack in the rope, so we should be able to lift the midpoint of the rope to some height (Figure 1). Imagine pinching the rope at its midpoint and raising the rope till it is taut. Question: To what height can you raise the midpoint? Try to estimate the answer without doing any computations; what does your intuition tell you?
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