In Longfellow’s novel Kavanagh, Mr. Churchill reads a word problem to his wife:
“In a lake the bud of a water-lily was observed, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits’ distance. Required the depth of the water.”
“That is charming, but must be very difficult,” she says. “I could not answer it.”
Is it? If a span is 9 inches and a cubit is 18 inches, how deep is the water?
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At the water’s surface, the bud marks one vertex of a right triangle. If the depth of the water is x inches, then (x + 9)2 = x2 + 362. If my algebra is good, then x = 67.5 inches.
Mr. Churchill was quoting the 12th-century Sanskrit text Lilavati, in which the problem first appeared, to show his wife that mathematics can be poetic:
In a certain lake swarming with geese and cranes,
The tip of a bud of lotus was seen one span above the water.
Forced by the wind, it gradually moved, and was submerged at a distance of two cubits.
O mathematician, tell quickly the depth of the water.
“There is something divine in the science of numbers,” Churchill tells her. “Like God, it holds the sea in the hollow of its hand. It measures the earth; it weighs the stars; it illumines the universe; it is law, it is order, it is beauty. And yet we imagine–that is, most of us–that its highest end and culminating point is book-keeping by double entry. It is our way of teaching it that makes it so prosaic.”
(Thanks, Shreevatsa.)
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