黄金比.再帰

黄金比 . 再帰 Lispで再帰と言えば fact, fib 黄金比は見つからないので考えた『 Scheme 手習い』読書会 #2 LT @manozo 15 AUG 2011

黄金比 1:1.618033988749894848 ,[object Object],[object Object],[object Object]

電　卓 ,[object Object],[object Object],[object Object]

連分数じーと見ていると再帰が使えそう (+ 1 (/ (+ 1 (/ (+ 1 (/ (+ 1 (/ (+ 1 (/ 　　　　　　 1.0) ))))))))) 1.625 ;; 再帰はお尻から

gaucheで黄金比 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

もうひとつ ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

factも同様に考えると 1 　　 1) )))) 0 1 (* 1 1) 1 2 (* 2 1) 2 6 (* 3 2) 3 24 (* 4 6) 4 120 (* 5 24) 5 値 (fact 5) n 再帰 (zero? n) 赤字が見えると理解できる

おまけ白金比, 青銅比 xyzzy で ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

 3.14159 26535 89793 23846... ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

 gauche 3.14159 26535 89793 23846... ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],;;(iota n 1) (use srfi-1 ) gosh> ;( time (pi 180000)) ; real 0.344 ; user 0.297 ; sys 0.000 3.141592653589793

 gauche 2 改造 3.14159 26535 89793 23846... ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],割り算っぽく if も式なので値を返す３項演算子風

これから再帰を考えた連分数はまさに再帰？ ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

まとめ ,[object Object],[object Object],[object Object]

参考 ,[object Object],[object Object],[object Object],[object Object],[object Object]

黄金比.再帰

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