Question

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. a + b a for a b>0 Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of nat- ural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts. For fun, here's a clip of the nostalgic Donald Duck in Mathmagic Land that explains the golden ratio / rectangle very well. The golden ratio is an irrational number, so the first 25 digits or so are: GR= 1.61803398874989484820... and the numbers just keep going. There are many ways to express the golden ratio numerically. The Fibonacci Sequence is a se- quence of numbers that adhere to the golden ratio in that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. Specifically, Fo = 0 and F1 = 1 and Fn = Fr-1 + Fn-2 for n >1 Often, Fo is omitted, and the Fibonacci sequence starts with Fi = F2 = 1. Thus, the beginning of the sequence is: 1,1,2,3,5,8, 13, 21, 34, 55, 89, 144,...

Done in matlab

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
format long
[GRn,fibo_n]=golden(10)
function [GRn,fibo_n]=golden(n)
v=zeros(1,n);
[~,f]=fibo(n);
for j=2:n
v(j)=(f(j))/f(j-1);
end
fibo_n=f;
GRn=v(end);
plot(1:n,v);
function [fibonum,f]=fibo(m)
f=[1,1];
for i=3:m
f(i)=f(i-1)+f(i-2);
end
fibonum=f(end);
end
  
end

- 5 x Pradeep - 0 X 56 Search Documentation Tax X ahk.m x bisectionmethodbypradeep.m X + | | A MATLAB R2018 HOME PLOTS APPS EDITOR Figure 1 D E L Find Files Insert E. fx Eile Edit View Insert Tools Desktop Window Help 3 Compare - -Go To - Comment % 99 O A BO E New Open Save Print F ind Indent 1 1 FILE NAVIGATE EDIT hal Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser AppLocker (Folder) 1 2 3 4 5 6 7 Workspace Com Name Value New to MATLAB? See resources for Getting Started, Hifibo_n (1,1,2,3,5,8,13,21,34,55] GRn 1.6176 1.617647058823529 8 9 10 fibo_n = 1 1 2 3 5 8 13 21 34 55 golden In 23 Col 4 ENG 3:27 AM IN 09/27/19 w OP - JP 4x 1 * Type here to search

Kindly revert for any queries

Thanks.