特殊的数.pptVIP

ACM 程序设计;今天，;每周一星（7）：;第八讲;主要内容;Fibonacci Number;Leonardo Fibonacci 1175-1250 ;You might ask where this came from? ; In Fibonaccis day, mathematical competitions and challenges were common. In 1225 Fibonacci took part in a tournament at Pisa ordered by the emperor himself, Frederick II. It was in just this type of competition that the following problem arose: ; Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months? ;January;February;March;April;May、June…;The number series is——;Some other pictures;Date;Date;Date;Date;Fibonacci number Golden Section;Date;white calla lily（白色马蹄莲）;Euphorbia(一种非洲植物，不常见);trillium （ 延龄草）;Columbine(耧斗菜);Bloodroot（一种罂粟科植物）;black-eyed susan;shasta daisy(大滨菊) with 21 petals;Ordinary field daisies(雏菊) have 34 petals ;The association of Fibonacci numbers and plants is not restricted to numbers of petals. ;If we draw horizontal lines through the axils, we can detect obvious stages of development in the plant. ;The number of branches at any stage of development is a Fibonacci number. ;Furthermore, the number of leaves in any stage will also be a Fibonacci number. ;sunflowers （向日葵）;Date;Date;Date;Fibonacci in geometrical style;Lucas Number;Edouard Lucas ;Question:;空间换时 间！！;Catalan number;先看一道题目：;示意图：;Easy or not ?; The Catalan numbers (1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, ...), named after Eugène Charles Catalan, arise in a number of problems in combinatorics. They can be computed using this formula: ;Eugène Charles Catalan;What can the Catalan numbers describe ?;1. The number of ways a polygon with n+2 sides can be cut into n triangles ;5 sides, 5 ways: ;7 sides, 42 ways:;2. the number of ways in which parentheses can be placed in a sequence of numbers to be multiplied, two at a time ; 5 numbers:;3.the number of rooted, trivalent trees with n+1 nodes ;5 n