Archimedes devised a method for computing by approximating a circle of radius 1/2 by successive...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Archimedes devised a method for computing π by approximating a circle of radius 1/2 by successive polygons and computing the perimeter of these polygons. This results in the iteration to 1+-1 tn+1 = tn and an approximation Tin = 6 -2” (a) Write a function that performs this calculation and plot πn versus n. On a separate graph, plot |π — π| vs. n using a log scale on the y-axis. The command to do this is semilogy. How large can you take n before improvements are limited by roundoff error? How accurately can you compute π? (b) What is the main source of error when n is large? (c) Rewrite the iteration in a way that will reduce this source of error. Repeat the calculation and plot the error in both results on one graph. How large can you take n this time before improvements are limited by roundoff error? How accurately can you compute π now? Archimedes devised a method for computing π by approximating a circle of radius 1/2 by successive polygons and computing the perimeter of these polygons. This results in the iteration to 1+-1 tn+1 = tn and an approximation Tin = 6 -2” (a) Write a function that performs this calculation and plot πn versus n. On a separate graph, plot |π — π| vs. n using a log scale on the y-axis. The command to do this is semilogy. How large can you take n before improvements are limited by roundoff error? How accurately can you compute π? (b) What is the main source of error when n is large? (c) Rewrite the iteration in a way that will reduce this source of error. Repeat the calculation and plot the error in both results on one graph. How large can you take n this time before improvements are limited by roundoff error? How accurately can you compute π now?
Expert Answer:
Answer rating: 100% (QA)
To address this problem well implement the given iteration and analyze the errors involved Well then suggest an improvement to reduce the error a Impl... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Do some amendment and enhance the given research paper: Table of Content Abstract..3 Action Research.4 Research Methodology and Design...5 Literature Review: NoSQL Database7 Proposal.7 Iteration 1..8...
-
A parametrization of a circle of radius 1 centered at (1, 0) in the xy-plane is given by x = 1 + cos t, y = sin t, for 0 t 2. Find the surface area when this curve is revolved about the y-axis.
-
Write MATLAB code of the question. Do all parts and show code with comments and also attach a screenshot of code and outputs. Using the results of Problem 4.13, verify the following properties of WN...
-
Discount is a discount appliance chain store that continually sells goods at a price below manufacturers suggested retail prices. A, B, and C, the three largest manufacturers of appliances, agree...
-
Determine the work required to transport \(10 \mathrm{~kg}\) of material from Earth to the ISS, the International Space Station, in orbit \(420 \mathrm{~km}\) above the Earth's surface.
-
Consider a source of flow in \(3 \mathrm{D}\) of strength \(S\) (dimensions \(L^{3} / T\) ), Then the flow is axisymmetric and independent of the \(\theta\)-direction in the spherical coordinate...
-
Victor Mineli, the new controller of Santorini Company, has reviewed the expected useful lives and salvage values of selected depreciable assets at the beginning of 2017. Here are his findings: All...
-
For 11, how do we know the vector should be pointing this way? For 12, I do not understand the explanation provided. What is meant by force in new direction? How do we know the trajectory is not...
-
You have been presented with the following set of financial statements for National Property Trust, a REIT that is about to make an initial stock offering to the public. This REIT specializes in the...
-
6. Configure link-local addresses dynamically. 7. Identify IPv6 addresses. 8. Implement a subnetted IPv6 addressing scheme. 9. Explain how ICMP is used to test network connectivity. 10. Use ping and...
-
You work for Sadioura & Napoleon Law Corp. The Lawyer you are assisting is Margaret Bonilla, who specializes in Corporate Law Today is February 25, (this year) A new client, Anita Desai, has decided...
-
A closed cylindrical tank, 1m diameter, 3m high, is full of water. It is rotating about its vertical axis with a speed of 120 rpm. Find the pressure, in Kpa, at the top just under the cover along the...
-
Set Up 1. Make a new main class called IA4_ParallelBubbleSort_LastName.java. 2. Copy an applicable sort method from a previous assignment and then alter it to take in a String Array for sorting plus...
-
Discuss the ethical considerations when developing Python applications, particularly in the context of data privacy and algorithmic bias.
-
We the information provided on the Walmart balance Sheet, I need to find the LIQUIDITY for the years 2015-2014-2013. Just the current ration and the quick ratio. What is liquidity and the formulas...
-
Jeremiah Restoration Company completed the following selected transactions during January: January 1. Established a petty cash fund of $900. 12. Cash sales for the day, according to cash registers,...
-
Which, if any, of the dichloroethene molecules drawn in Data Table II (3.) (4.) and (5.) are geometric isomers? A. B. C. D. cis-1,2-dichloroethene and trans-1,2-dichloroethene...
-
For the following exercises, the cost of producing x cellphones is described by the function C(x) = x 2 4x + 1000. Find the average rate of change in the total cost as x changes from x = 10 to x =...
-
For the following exercises, convert the complex number from polar to rectangular form. z = 3cis(240)
-
For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. cot x; sin x
-
What are the numbers of observations in each of the five categories that rate the respondents level of job satisfaction?
-
Which of the seven store departments had the most customer visits, and what was this number?
-
How many individuals are in each of the five different credit card categories?
Study smarter with the SolutionInn App