Lazy Caterer's Sequence
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a circle (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point, but seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, see arrangement of hyperplanes.
The analogue of this sequence in 3 dimensions is the cake number.
Read more about Lazy Caterer's Sequence: Formula and Sequence, Proof
Famous quotes containing the words lazy and/or sequence:
“In clear weather the laziest may look across the Bay as far as Plymouth at a glance, or over the Atlantic as far as human vision reaches, merely raising his eyelids; or if he is too lazy to look after all, he can hardly help hearing the ceaseless dash and roar of the breakers. The restless ocean may at any moment cast up a whale or a wrecked vessel at your feet. All the reporters in the world, the most rapid stenographers, could not report the news it brings.”
—Henry David Thoreau (1817–1862)
“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a sequence of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”
—Philip Roth (b. 1933)