Significance
Newton's formula is of interest because it is the straightforward and natural differences-version of Taylor's polynomial. Taylor's polynomial tells where a function will go, based on its y value, and its derivatives (its rate of change, and the rate of change of its rate of change, etc.) at one particular x value. Newton's formula is Taylor's polynomial based on finite differences instead of instantaneous rates of change.
Read more about this topic: Newton Polynomial
Famous quotes containing the word significance:
“Of what significance the light of day, if it is not the reflection of an inward dawn?—to what purpose is the veil of night withdrawn, if the morning reveals nothing to the soul? It is merely garish and glaring.”
—Henry David Thoreau (1817–1862)
“The hypothesis I wish to advance is that ... the language of morality is in ... grave disorder.... What we possess, if this is true, are the fragments of a conceptual scheme, parts of which now lack those contexts from which their significance derived. We possess indeed simulacra of morality, we continue to use many of the key expressions. But we have—very largely if not entirely—lost our comprehension, both theoretical and practical, of morality.”
—Alasdair Chalmers MacIntyre (b. 1929)
“History is the interpretation of the significance that the past has for us.”
—Johan Huizinga (1872–1945)