What do Fibonacci numbers, 1,1,2,3,5, etc. have to do with the golden ratio, 1.618??? What's the relationship?
回答 (4)
2015-12-29 7:11 am
The ratio of the numbers approach the golden ratio
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/
2015-12-29 10:13 am
The relationships are:
1. As n increases F(n+1)/F(n) approaches ϕ
2. F(n) = (ϕⁿ - (-ϕ)⁻ⁿ) / √5
3. ϕⁿ = F(n)ϕ + F(n-1)
Starting from F(0)=0 and F(1)=1, and where ϕ is the Golden Ratio, with the value (1+√5)/2
1. As n increases F(n+1)/F(n) approaches ϕ
2. F(n) = (ϕⁿ - (-ϕ)⁻ⁿ) / √5
3. ϕⁿ = F(n)ϕ + F(n-1)
Starting from F(0)=0 and F(1)=1, and where ϕ is the Golden Ratio, with the value (1+√5)/2
2015-12-29 7:29 am
The ratio of the any number, n in this sequence to its prior number tends to be the Golden ratio as n tends to infinity.
2015-12-29 9:30 am
The ratio of the numbers approach the golden ratio
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/
if you have more maths question use mathqu homework support app in app store this is the best app to get answers from live tutors who write step by step maths answers search for mathqu in app store
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615+
34/21 = 1.619+ etc/
if you have more maths question use mathqu homework support app in app store this is the best app to get answers from live tutors who write step by step maths answers search for mathqu in app store
收錄日期: 2021-04-21 16:04:18
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