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)
“A man should not go where he cannot carry his whole sphere or society with him,Mnot bodily, the whole circle of his friends, but atmospherically. He should preserve in a new company the same attitude of mind and reality of relation, which his daily associates draw him to, else he is shorn of his best beams, and will be an orphan in the merriest club.”
—Ralph Waldo Emerson (1803–1882)
“Adults understandably assume that the level of verbal proficiency a five-year-old displays represents his level of proficiency in all areas of functioning—if he talks like an adult, he must think and feel like one. However, five-year-olds,... belie the promise of adult-like behavior with their child-like, impulsive actions.”
—Dorothy H. Cohen (20th century)