The golden ratio (4) has intrigued many people (not just mathematicians!) for over two millennia. The...

 

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The golden ratio (4) has intrigued many people (not just mathematicians!) for over two millennia. The ratio is purported to occur naturally in many places, e.g., proportions within animal and human bodies, plants, and shells. The earliest deliberate use of the golden ratio by humans is considered to be made by Phidias (490-430 BC) in his construction of the Parthenon statues. Give an illustration of the golden ratio in terms of line segments. The golden ratio can be expressed as an infinite continued fraction: 6=1+. 1+ 1+ 1 4 = 1+ 1 1+ 1 1 1+ We notice that the (overall) denominator of this expression is in fact ; hence we can write Solve this equation to derive an analytical formula for . Starting from an initial iterate of x = 1, write a MATLAB script that implements a while loop to compute to within a tolerance tol by the iteration x = 1 + 1/x. How many iterations does your loop take to converge to within 10eps of p? Activate Wir Go to Settings to The golden ratio (4) has intrigued many people (not just mathematicians!) for over two millennia. The ratio is purported to occur naturally in many places, e.g., proportions within animal and human bodies, plants, and shells. The earliest deliberate use of the golden ratio by humans is considered to be made by Phidias (490-430 BC) in his construction of the Parthenon statues. Give an illustration of the golden ratio in terms of line segments. The golden ratio can be expressed as an infinite continued fraction: 6=1+. 1+ 1+ 1 4 = 1+ 1 1+ 1 1 1+ We notice that the (overall) denominator of this expression is in fact ; hence we can write Solve this equation to derive an analytical formula for . Starting from an initial iterate of x = 1, write a MATLAB script that implements a while loop to compute to within a tolerance tol by the iteration x = 1 + 1/x. How many iterations does your loop take to converge to within 10eps of p? Activate Wir Go to Settings to