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first chapter completed!

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sarabander committed Jul 21, 2011
1 parent 2732339 commit f11bc009a25deb29cfcf52946fa47cdf9735d8cb
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  1. +7 βˆ’7 1.3/Ex1.35.scm
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-;; The golden ratio comes from this: 𝛗 = a/b = (a + b)/a = 1 + b/a = 1 + 1/𝛗.
-;; It is already clear from definition that 𝛗 is a fixed point of x ↦ 1 + 1/x.
-;; Another way to prove this is to use the exact value of 𝛗 in x ↦ 1 + 1/x.
+;; The golden ratio comes from this: πœ‘ = a/b = (a + b)/a = 1 + b/a = 1 + 1/πœ‘.
+;; It is already clear from definition that πœ‘ is a fixed point of x ↦ 1 + 1/x.
+;; Another way to prove this is to use the exact value of πœ‘ in x ↦ 1 + 1/x.
-;; Multiplying both sides of 𝛗 = 1 + 1/𝛗 by 𝛗, we get 𝛗² = 𝛗 + 1.
+;; Multiplying both sides of πœ‘ = 1 + 1/πœ‘ by πœ‘, we get πœ‘Β² = πœ‘ + 1.
;; Which numerical values satisfy this equation?
-;; Rearranging, we get 𝛗² - 𝛗 - 1 = 0, where 𝛗 = (1 Β± √5)/2 β‰ˆ 1.6180...
+;; Rearranging, we get πœ‘Β² - πœ‘ - 1 = 0, where πœ‘ = (1 Β± √5)/2 β‰ˆ 1.6180...
;; We will put this value into the right side of x ↦ 1 + 1/x and hope to
-;; arrive at the left side: 1 + 1/𝛗 = 1 + 2/(1 Β± √5) = (1 Β± √5 + 2)/(1 Β± √5)
+;; arrive at the left side: 1 + 1/πœ‘ = 1 + 2/(1 Β± √5) = (1 Β± √5 + 2)/(1 Β± √5)
;; (3 Β± √5)(1 βˆ“ √5) 3 βˆ“ 3√5 Β± √5 - 5 -2 βˆ“ 2√5 1 Β± √5
-;; = ---------------- = ---------------- = -------- = ------ = 𝛗. ∎
+;; = ---------------- = ---------------- = -------- = ------ = πœ‘. ∎
;; (1 Β± √5)(1 βˆ“ √5) 1 - 5 -4 2
;; We will now compute the golden ratio using the provided procedure:

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