The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to Vladimir Arnold and the folding of a Russian ruble. Some versions of the problem were solved by Robert J. Lang, Svetlana Krat, Alexey S. Tarasov, and Ivan Yaschenko. One form of the problem remains open.
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Famous quotes containing the words napkin, folding and/or problem:
“Again brutish necessity wipes its hands
Upon the napkin of a dirty cause,”
—Derek Walcott (b. 1930)
“There’s only one way for an individual to remain upright, not to fall to pieces, not to sink into the mire of self-oblivion ... or self-contempt. That’s calmly to turn away from everything, to say, “Enough!” and, folding one’s useless arms across one’s empty breast, to retain the ultimate, the sole attainable virtue, the virtue of recognizing one’s own insignificance.”
—Ivan Sergeevich Turgenev (1818–1883)
“The disesteem into which moralists have fallen is due at bottom to their failure to see that in an age like this one the function of the moralist is not to exhort men to be good but to elucidate what the good is. The problem of sanctions is secondary.”
—Walter Lippmann (1889–1974)