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:
“The dreary flies, lazy and casual,
Stick to the ceiling, buzz along the wall.
O heart, the spider shuffles from the mould
Weaving, between the pinks and grapes, his pall.”
—Allen Tate (1899–1979)
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)