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:
“What makes it so plausible to assume that hypocrisy is the vice of vices is that integrity can indeed exist under the cover of all other vices except this one. Only crime and the criminal, it is true, confront us with the perplexity of radical evil; but only the hypocrite is really rotten to the core.”
—Hannah Arendt (1906–1975)
“Chaucer’s remarkably trustful and affectionate character appears in his familiar, yet innocent and reverent, manner of speaking of his God. He comes into his thought without any false reverence, and with no more parade than the zephyr to his ear.... There is less love and simple, practical trust in Shakespeare and Milton. How rarely in our English tongue do we find expressed any affection for God! Herbert almost alone expresses it, “Ah, my dear God!””
—Henry David Thoreau (1817–1862)
“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)