Plausible But False Examples
Some plausible relations hold to a high degree of accuracy, but are still not true. One example is:
The two sides of this expression only differ after the 42nd decimal place.
Another example is that the maximum height (maximum absolute value of coefficients) of all the factors of xn − 1 appears to be the same as height of nth cyclotomic polynomial. This was shown by computer to be true for n < 10000 and was expected to be true for all n. However, a larger computer search showed that this equality fails to hold for n = 14235, when the height of the nth cyclotomic polynomial is 2, but maximum height of the factors is 3.
Read more about this topic: Experimental Mathematics
Famous quotes containing the words plausible, false and/or examples:
“The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with cylinder oil, and coat their outsides with sprayed rubber film, and let them statically await the next emergency.”
—Norbert Wiener (1894–1964)
“That author who draws a character, even though to common view incongruous in its parts, as the flying-squirrel, and, at different periods, as much at variance with itself as the caterpillar is with the butterfly into which it changes, may yet, in so doing, be not false but faithful to facts.”
—Herman Melville (1819–1891)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)