Answer The value of ratios of two continuous terms in a fibonacci sequence 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , ... as the terms getting larger is approximate equal to 1.618 called as golden ratio. Explanation Given information: The fibonacci number sequence is given as 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , ... There is one computer programme is also given to run it. Formula used: In the fibonacci number sequence the next term is sum of the last two terms, which can be represents by this, 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , .... Calculation: Consider the given computer program and run it in the operating system. Now, result comes out to be, Number n-th Fibonacci Number f(n)/f(n-1) f(n-1)/f(n) f(n)/f(n-1) Phi=1.618… f(n-1)/f(n) Phi=0.618… f-0 1 f-1 1 1 1 1 1.618034 1 0.618034 f-2 2 2 0.5 2 1.618034 0.5 0.618034 f-3 3 1.5 0.666667 1.5 1.618034 0.666667 0.618034 f-4 5 1.666667 0.6 1.666667 1.618034 0.6 0.618034 f-5 8 1.6 0.625 1.6 1.618034 0.625 0.618034 f-6 13 1.625 0.615385 1.625 1.618034 0.615385 0.618034 f-7 21 1.615385 0.619048 1.615385 1.618034 0.619048 0.618034 f-8 34 1.619048 0.617647 1.619048 1.618034 0.617647 0.618034 f-9 55 1.617647 0.618182 1.617647 1.618034 0.618182 0.618034 f-10 89 1.618182 0.617978 1.618182 1.618034 0.617978 0.618034 f-11 144 1.617978 0.618056 1.617978 1.618034 0.618056 0.618034 f-12 233 1.618056 0.618026 1.618056 1.618034 0.618026 0.618034 f-13 377 1.618026 0.618037 1.618026 1.618034 0.618037 0.618034 f-14 610 1.618037 0.618033 1.618037 1.618034 0.618033 0.618034 f-15 987 1.618033 0.618034 1.618033 1.618034 0.618034 0.618034 f-16 1597 1.618034 0.618034 1.618034 1.618034 0.618034 0.618034 f-17 2584 1.618034 0.618034 1.618034 1.618034 0.618034 0.618034 f-18 4181 1.618034 0.618034 1.618034 1.618034 0.618034 0.618034 It is very clear from the above table that ratio between two continuous successor and Predecessor term is approximate equal to 1.618. Therefore, the value of ratios of two continuous terms in a fibonacci sequence 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , ... as the terms getting larger is approximate equal to 1.618 called as golden ratio.

McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Question

Chapter 7.4, Problem 1AE

To determine

To calculate: The value of ratios of two continuous terms in a fibonacci sequence 1,1,2,3,5,8,13,21,... as the terms getting larger with the help of computer program.

Expert Solution & Answer

Answer to Problem 1AE

The value of ratios of two continuous terms in a fibonacci sequence 1,1,2,3,5,8,13,21,... as the terms getting larger is approximate equal to 1.618 called as golden ratio.

Explanation of Solution

Given information:

The fibonacci number sequence is given as 1,1,2,3,5,8,13,21,...

There is one computer programme is also given to run it.

Formula used:

In the fibonacci number sequence the next term is sum of the last two terms, which can be represents by this,

1,1,2,3,5,8,13,21,34,55,89,....

Calculation:

Consider the given computer program and run it in the operating system.

Now, result comes out to be,

Number	n-th Fibonacci Number	f(n)/f(n-1)	f(n-1)/f(n)	f(n)/f(n-1)	Phi=1.618…	f(n-1)/f(n)	Phi=0.618…
f-0	1
f-1	1	1	1	1	1.618034	1	0.618034
f-2	2	2	0.5	2	1.618034	0.5	0.618034
f-3	3	1.5	0.666667	1.5	1.618034	0.666667	0.618034
f-4	5	1.666667	0.6	1.666667	1.618034	0.6	0.618034
f-5	8	1.6	0.625	1.6	1.618034	0.625	0.618034
f-6	13	1.625	0.615385	1.625	1.618034	0.615385	0.618034
f-7	21	1.615385	0.619048	1.615385	1.618034	0.619048	0.618034
f-8	34	1.619048	0.617647	1.619048	1.618034	0.617647	0.618034
f-9	55	1.617647	0.618182	1.617647	1.618034	0.618182	0.618034
f-10	89	1.618182	0.617978	1.618182	1.618034	0.617978	0.618034
f-11	144	1.617978	0.618056	1.617978	1.618034	0.618056	0.618034
f-12	233	1.618056	0.618026	1.618056	1.618034	0.618026	0.618034
f-13	377	1.618026	0.618037	1.618026	1.618034	0.618037	0.618034
f-14	610	1.618037	0.618033	1.618037	1.618034	0.618033	0.618034
f-15	987	1.618033	0.618034	1.618033	1.618034	0.618034	0.618034
f-16	1597	1.618034	0.618034	1.618034	1.618034	0.618034	0.618034
f-17	2584	1.618034	0.618034	1.618034	1.618034	0.618034	0.618034
f-18	4181	1.618034	0.618034	1.618034	1.618034	0.618034	0.618034

It is very clear from the above table that ratio between two continuous successor and Predecessor term is approximate equal to 1.618.

Therefore, the value of ratios of two continuous terms in a fibonacci sequence 1,1,2,3,5,8,13,21,... as the terms getting larger is approximate equal to 1.618 called as golden ratio.

Chapter 7.4, Problem 2C

Chapter 7.4, Problem 2AE

Chapter 7 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 7.1 - Prob. 1CE Ch. 7.1 - Prob. 2CE Ch. 7.1 - Prob. 3CE Ch. 7.1 - Prob. 4CE Ch. 7.1 - Prob. 5CE Ch. 7.1 - Prob. 6CE Ch. 7.1 - Prob. 7CE Ch. 7.1 - Prob. 8CE Ch. 7.1 - Prob. 9CE Ch. 7.1 - Prob. 10CE

Ch. 7.1 - Prob. 11CE Ch. 7.1 - Prob. 12CE Ch. 7.1 - Prob. 13CE Ch. 7.1 - Prob. 14CE Ch. 7.1 - Prob. 15CE Ch. 7.1 - Prob. 16CE Ch. 7.1 - Prob. 17CE Ch. 7.1 - Prob. 18CE Ch. 7.1 - Prob. 1WE Ch. 7.1 - Prob. 2WE Ch. 7.1 - Prob. 3WE Ch. 7.1 - Prob. 4WE Ch. 7.1 - Prob. 5WE Ch. 7.1 - Prob. 6WE Ch. 7.1 - Prob. 7WE Ch. 7.1 - Prob. 8WE Ch. 7.1 - Prob. 9WE Ch. 7.1 - Prob. 10WE Ch. 7.1 - Prob. 11WE Ch. 7.1 - Prob. 12WE Ch. 7.1 - Prob. 13WE Ch. 7.1 - Prob. 14WE Ch. 7.1 - Prob. 15WE Ch. 7.1 - Prob. 16WE Ch. 7.1 - Prob. 17WE Ch. 7.1 - Prob. 18WE Ch. 7.1 - Prob. 19WE Ch. 7.1 - Prob. 20WE Ch. 7.1 - Prob. 21WE Ch. 7.1 - Prob. 22WE Ch. 7.1 - Prob. 23WE Ch. 7.1 - Prob. 24WE Ch. 7.1 - Prob. 25WE Ch. 7.1 - Prob. 26WE Ch. 7.1 - Prob. 27WE Ch. 7.1 - Prob. 28WE Ch. 7.1 - Prob. 29WE Ch. 7.1 - Prob. 30WE Ch. 7.1 - Prob. 31WE Ch. 7.1 - Prob. 32WE Ch. 7.1 - Prob. 33WE Ch. 7.1 - Prob. 34WE Ch. 7.1 - Prob. 35WE Ch. 7.1 - Prob. 36WE Ch. 7.2 - Prob. 1CE Ch. 7.2 - Prob. 2CE Ch. 7.2 - Prob. 3CE Ch. 7.2 - Prob. 4CE Ch. 7.2 - Prob. 5CE Ch. 7.2 - Prob. 6CE Ch. 7.2 - Prob. 7CE Ch. 7.2 - Prob. 8CE Ch. 7.2 - Prob. 9CE Ch. 7.2 - Prob. 10CE Ch. 7.2 - Prob. 11CE Ch. 7.2 - Prob. 12CE Ch. 7.2 - Prob. 13CE Ch. 7.2 - Prob. 14CE Ch. 7.2 - Prob. 15CE Ch. 7.2 - Prob. 16CE Ch. 7.2 - Prob. 1WE Ch. 7.2 - Prob. 2WE Ch. 7.2 - Prob. 3WE Ch. 7.2 - Prob. 4WE Ch. 7.2 - Prob. 5WE Ch. 7.2 - Prob. 6WE Ch. 7.2 - Prob. 7WE Ch. 7.2 - Prob. 8WE Ch. 7.2 - Prob. 9WE Ch. 7.2 - Prob. 10WE Ch. 7.2 - Prob. 11WE Ch. 7.2 - Prob. 12WE Ch. 7.2 - Prob. 13WE Ch. 7.2 - Prob. 14WE Ch. 7.2 - Prob. 15WE Ch. 7.2 - Prob. 16WE Ch. 7.2 - Prob. 17WE Ch. 7.2 - Prob. 18WE Ch. 7.2 - Prob. 19WE Ch. 7.2 - Prob. 20WE Ch. 7.2 - Prob. 21WE Ch. 7.2 - Prob. 22WE Ch. 7.2 - Prob. 23WE Ch. 7.2 - Prob. 24WE Ch. 7.2 - Prob. 25WE Ch. 7.2 - Prob. 26WE Ch. 7.2 - Prob. 27WE Ch. 7.2 - Prob. 28WE Ch. 7.2 - Prob. 29WE Ch. 7.2 - Prob. 30WE Ch. 7.2 - Prob. 31WE Ch. 7.2 - Prob. 32WE Ch. 7.2 - Prob. 33WE Ch. 7.2 - Prob. 34WE Ch. 7.2 - Prob. 35WE Ch. 7.2 - Prob. 36WE Ch. 7.2 - Prob. 37WE Ch. 7.2 - Prob. 38WE Ch. 7.2 - Prob. 39WE Ch. 7.2 - Prob. 40WE Ch. 7.2 - Prob. 41WE Ch. 7.2 - Prob. 42WE Ch. 7.2 - Prob. 43WE Ch. 7.3 - Prob. 1CE Ch. 7.3 - Prob. 2CE Ch. 7.3 - Prob. 3CE Ch. 7.3 - Prob. 4CE Ch. 7.3 - Prob. 5CE Ch. 7.3 - Prob. 6CE Ch. 7.3 - Prob. 7CE Ch. 7.3 - Prob. 8CE Ch. 7.3 - Prob. 9CE Ch. 7.3 - Prob. 10CE Ch. 7.3 - Prob. 1WE Ch. 7.3 - Prob. 2WE Ch. 7.3 - Prob. 3WE Ch. 7.3 - Prob. 4WE Ch. 7.3 - Prob. 5WE Ch. 7.3 - Prob. 6WE Ch. 7.3 - Prob. 7WE Ch. 7.3 - Prob. 8WE Ch. 7.3 - Prob. 9WE Ch. 7.3 - Prob. 10WE Ch. 7.3 - Prob. 11WE Ch. 7.3 - Prob. 12WE Ch. 7.3 - Prob. 13WE Ch. 7.3 - Prob. 14WE Ch. 7.3 - Prob. 15WE Ch. 7.3 - Prob. 16WE Ch. 7.3 - Prob. 17WE Ch. 7.3 - Prob. 18WE Ch. 7.3 - Prob. 19WE Ch. 7.3 - Prob. 20WE Ch. 7.3 - Prob. 21WE Ch. 7.3 - Prob. 22WE Ch. 7.3 - Prob. 23WE Ch. 7.3 - Prob. 24WE Ch. 7.3 - Prob. 25WE Ch. 7.3 - Prob. 26WE Ch. 7.3 - Prob. 27WE Ch. 7.3 - Prob. 28WE Ch. 7.3 - Prob. 29WE Ch. 7.3 - Prob. 30WE Ch. 7.3 - Prob. 31WE Ch. 7.3 - Prob. 32WE Ch. 7.3 - Prob. 33WE Ch. 7.3 - Prob. 34WE Ch. 7.3 - Prob. 35WE Ch. 7.3 - Prob. 36WE Ch. 7.3 - Prob. 37WE Ch. 7.3 - Prob. 1ST1 Ch. 7.3 - Prob. 2ST1 Ch. 7.3 - Prob. 3ST1 Ch. 7.3 - Prob. 4ST1 Ch. 7.3 - Prob. 5ST1 Ch. 7.3 - Prob. 6ST1 Ch. 7.3 - Prob. 7ST1 Ch. 7.3 - Prob. 8ST1 Ch. 7.3 - Prob. 9ST1 Ch. 7.3 - Prob. 10ST1 Ch. 7.3 - Prob. 11ST1 Ch. 7.3 - Prob. 12ST1 Ch. 7.3 - Prob. 13ST1 Ch. 7.3 - Prob. 14ST1 Ch. 7.3 - Prob. 15ST1 Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.4 - Prob. 1CE Ch. 7.4 - Prob. 2CE Ch. 7.4 - Prob. 3CE Ch. 7.4 - Prob. 4CE Ch. 7.4 - Prob. 5CE Ch. 7.4 - Prob. 6CE Ch. 7.4 - Prob. 7CE Ch. 7.4 - Prob. 8CE Ch. 7.4 - Prob. 9CE Ch. 7.4 - Prob. 10CE Ch. 7.4 - Prob. 11CE Ch. 7.4 - Prob. 12CE Ch. 7.4 - Prob. 13CE Ch. 7.4 - Prob. 1WE Ch. 7.4 - Prob. 2WE Ch. 7.4 - Prob. 3WE Ch. 7.4 - Prob. 4WE Ch. 7.4 - Prob. 5WE Ch. 7.4 - Prob. 6WE Ch. 7.4 - Prob. 7WE Ch. 7.4 - Prob. 8WE Ch. 7.4 - Prob. 9WE Ch. 7.4 - Prob. 10WE Ch. 7.4 - Prob. 11WE Ch. 7.4 - Prob. 12WE Ch. 7.4 - Prob. 13WE Ch. 7.4 - Prob. 14WE Ch. 7.4 - Prob. 15WE Ch. 7.4 - Prob. 16WE Ch. 7.4 - Prob. 17WE Ch. 7.4 - Prob. 18WE Ch. 7.4 - Prob. 19WE Ch. 7.4 - Prob. 20WE Ch. 7.4 - Prob. 21WE Ch. 7.4 - Prob. 22WE Ch. 7.4 - Prob. 23WE Ch. 7.4 - Prob. 24WE Ch. 7.4 - Prob. 25WE Ch. 7.4 - Prob. 26WE Ch. 7.4 - Prob. 27WE Ch. 7.4 - Prob. 28WE Ch. 7.4 - Prob. 29WE Ch. 7.4 - Prob. 30WE Ch. 7.4 - Prob. 31WE Ch. 7.4 - Prob. 32WE Ch. 7.4 - Prob. 33WE Ch. 7.4 - Prob. 34WE Ch. 7.4 - Prob. 35WE Ch. 7.4 - Prob. 1C Ch. 7.4 - Prob. 2C Ch. 7.4 - Prob. 1AE Ch. 7.4 - Prob. 2AE Ch. 7.4 - Prob. 3AE Ch. 7.4 - Prob. 4AE Ch. 7.4 - Prob. 1BE Ch. 7.4 - Prob. 2BE Ch. 7.4 - Prob. 3BE Ch. 7.4 - Prob. 4BE Ch. 7.5 - Prob. 1CE Ch. 7.5 - Prob. 2CE Ch. 7.5 - Prob. 3CE Ch. 7.5 - Prob. 4CE Ch. 7.5 - Prob. 5CE Ch. 7.5 - Prob. 6CE Ch. 7.5 - Prob. 7CE Ch. 7.5 - Prob. 8CE Ch. 7.5 - Prob. 9CE Ch. 7.5 - Prob. 1WE Ch. 7.5 - Prob. 2WE Ch. 7.5 - Prob. 3WE Ch. 7.5 - Prob. 4WE Ch. 7.5 - Prob. 5WE Ch. 7.5 - Prob. 6WE Ch. 7.5 - Prob. 7WE Ch. 7.5 - Prob. 8WE Ch. 7.5 - Prob. 9WE Ch. 7.5 - Prob. 10WE Ch. 7.5 - Prob. 11WE Ch. 7.5 - 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Prob. 27WE Ch. 7.6 - Prob. 28WE Ch. 7.6 - Prob. 29WE Ch. 7.6 - Prob. 30WE Ch. 7.6 - Prob. 31WE Ch. 7.6 - Prob. 32WE Ch. 7.6 - Prob. 33WE Ch. 7.6 - Prob. 1ST2 Ch. 7.6 - Prob. 2ST2 Ch. 7.6 - Prob. 3ST2 Ch. 7.6 - Prob. 4ST2 Ch. 7.6 - Prob. 5ST2 Ch. 7.6 - Prob. 6ST2 Ch. 7.6 - Prob. 7ST2 Ch. 7.6 - Prob. 8ST2 Ch. 7.6 - Prob. 9ST2 Ch. 7.6 - Prob. 10ST2 Ch. 7.6 - Prob. 11ST2 Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7 - Prob. 1CR Ch. 7 - Prob. 2CR Ch. 7 - Prob. 3CR Ch. 7 - Prob. 4CR Ch. 7 - Prob. 5CR Ch. 7 - Prob. 6CR Ch. 7 - Prob. 7CR Ch. 7 - Prob. 8CR Ch. 7 - Prob. 9CR Ch. 7 - Prob. 10CR Ch. 7 - Prob. 11CR Ch. 7 - Prob. 12CR Ch. 7 - Prob. 13CR Ch. 7 - Prob. 14CR Ch. 7 - Prob. 15CR Ch. 7 - Prob. 16CR Ch. 7 - Prob. 17CR Ch. 7 - Prob. 18CR Ch. 7 - Prob. 19CR Ch. 7 - Prob. 20CR Ch. 7 - Prob. 21CR Ch. 7 - Prob. 22CR Ch. 7 - Prob. 23CR Ch. 7 - Prob. 24CR Ch. 7 - Prob. 1CT Ch. 7 - Prob. 2CT Ch. 7 - Prob. 3CT Ch. 7 - 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