Two quantities a and b are said to be in the golden ratio if (a+b)ais equal to ab. Assuming a and b are line segments, the golden section is a line segment divided according to the golden ratio: The total length (a + b) is to the longer segment a as a is to the shorter segment b. It turns out that the ratios of successive terms of the Fibonacci sequence approximate the golden ratio. That is to say F(n+1)F(n) is, in the limit, the golden ratio, where F(n) is the nth number of the Fibonacci sequence. Consider the function below that computes an approximation to the golden ratio using the (n-1) and (n-2) numbers in the Fibonacci sequence: double golden(int n) { } double ratio; if (n <= 2) { ratio = 1.0; } else { ratio = ((1.0) * fib(n-1)) / (1.0 * fib(n - 2)); } return ratio; Which statements are true? 1.The function golden is recursive II.The function goldenis a helper function III.The function goldenassumes that another function fib computes the Fibonacci numbers required to compute the ratio
Two quantities a and b are said to be in the golden ratio if (a+b)ais equal to ab. Assuming a and b are line segments, the golden section is a line segment divided according to the golden ratio: The total length (a + b) is to the longer segment a as a is to the shorter segment b. It turns out that the ratios of successive terms of the Fibonacci sequence approximate the golden ratio. That is to say F(n+1)F(n) is, in the limit, the golden ratio, where F(n) is the nth number of the Fibonacci sequence. Consider the function below that computes an approximation to the golden ratio using the (n-1) and (n-2) numbers in the Fibonacci sequence: double golden(int n) { } double ratio; if (n <= 2) { ratio = 1.0; } else { ratio = ((1.0) * fib(n-1)) / (1.0 * fib(n - 2)); } return ratio; Which statements are true? 1.The function golden is recursive II.The function goldenis a helper function III.The function goldenassumes that another function fib computes the Fibonacci numbers required to compute the ratio
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Transcribed Image Text:Two quantities a and b are said to be in the golden ratio if (a+b)ais equal to
ab. Assuming a and b are line segments, the golden section is a line segment divided
according to the golden ratio: The total length (a + b) is to the longer segment a as a
is to the shorter segment b. It turns out that the ratios of successive terms of the
Fibonacci sequence approximate the golden ratio. That is to say F(n+1)F(n) is, in the
limit, the golden ratio, where F(n) is the nth number of the Fibonacci
sequence. Consider the function below that computes an approximation to the
golden ratio using the (n-1) and (n-2) numbers in the Fibonacci sequence:
double golden(int n)
{
}
double ratio;
if (n <= 2) { ratio = 1.0; }
else { ratio = ((1.0) * fib(n-1)) / (1.0 * fib(n - 2)); }
return ratio;
Which statements are true?
1.The function golden is recursive
II.The function goldenis a helper function
III.The function goldenassumes that another function fib computes the Fibonacci
numbers required to compute the ratio
Transcribed Image Text:sequence. Consider the function below that computes an approximation to the
golden ratio using the (n-1) and (n-2) numbers in the Fibonacci sequence:
double golden (int n)
{
}
double ratio;
if (n <= 2) { ratio = 1.0; }
else { ratio = ((1.0) * fib(n - 1)) / (1.0 * fib(n - 2)); }
return ratio;
Which statements are true?
I.The function golden is recursive
II.The function goldenis a helper function
III.The function goldenassumes that another function fib computes the Fibonacci
numbers required to compute the ratio
O1, 11
I, III
II, III
I, II, III
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