In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides, in such a way as to maximise the number of areas created by the edges and diagonals, has a solution by an inductive method.
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Famous quotes containing the words dividing, circle and/or areas:
“If you stand right fronting and face to face to a fact, you will see the sun glimmer on both its surfaces, as if it were a cimeter, and feel its sweet edge dividing you through the heart and marrow, and so you will happily conclude your mortal career. Be it life or death, we crave only reality. If we are really dying, let us hear the rattle in our throats and feel cold in the extremities; if we are alive, let us go about our business.”
—Henry David Thoreau (1817–1862)
“It is a good lesson—though it may often be a hard one—for a man who has dreamed of literary fame, and of making for himself a rank among the world’s dignitaries by such means, to step aside out of the narrow circle in which his claims are recognized, and to find how utterly devoid of all significance, beyond that circle, is all that he achieves, and all he aims at.”
—Nathaniel Hawthorne (1804–1864)
“Helping children at a level of genuine intellectual inquiry takes imagination on the part of the adult. Even more, it takes the courage to become a resource in unfamiliar areas of knowledge and in ones for which one has no taste. But parents, no less than teachers, must respect a child’s mind and not exploit it for their own vanity or ambition, or to soothe their own anxiety.”
—Dorothy H. Cohen (20th century)