StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...

Buffron Needle Problem - Essay Example

Cite this document
Summary
He was a French mathematician and naturalist who lived between 1707 and 1788. In 1777, he came up with Buffon Needle Problem, named after him to find out the probability…
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER93.6% of users find it useful
Buffron Needle Problem
Read Text Preview

Extract of sample "Buffron Needle Problem"

Download file to see previous pages

The assumption would be that the lines are parallel to the x-axis. Two variables exist in this scenario; the angle with which the needle would be tilted to the lines, Ɵ, and the distance between the closest line and the center, which would never exceed half the distance between the equidistant lines (See fig. 2 below) The assumption is that the needle would land at a random point between the lines and the angle of inclination would be another random variable. It should further be assumed that the random variables are a result of uniform distribution.

This picture depicts the needle missing the line and the needle could only be on the line if the distance closest to a line, D would be less than or equal to ½SinƟ, that is D ≤ ½SinƟ. This could be illustrated better using figure 3 below. From this, the values representing a hit would occur below or on the curve, D ≤ 1/2SinƟ. The probability of hitting the line would be computed as a ratio of the shaded curve to the area of the entire rectangle. The area under the curve would be computed using integrals between zero and π.

This will give a result of 1. The rectangle would have an area of ½π. The probability of hitting the line would therefore be 1/ (½π) = 2/π, which is approximately 0.6366. To work out π, the number of needle drops, say N would be multiplied by two and then divided by the number of hits, N’. That is: This would be a situation where the needle is long and its length, l, would be greater than the distance between the equidistant lines. Hence, x = l/d > l. The probability that the needle would intersect a line would be computed using the expression below: Consider the size parameter x = l/d.

Taking N as the number of crossings and n as the tosses made by a short needle of size parameter x, then N would have a binomial distribution as a function of n and 2x/π. The point estimator with regard to

...Download file to see next pages Read More
Tags
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 words”, n.d.)
Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 words. Retrieved from https://studentshare.org/mathematics/1586188-buffron-needle-problem
(Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 Words)
Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 Words. https://studentshare.org/mathematics/1586188-buffron-needle-problem.
“Buffron Needle Problem Essay Example | Topics and Well Written Essays - 1500 Words”, n.d. https://studentshare.org/mathematics/1586188-buffron-needle-problem.
  • Cited: 0 times

CHECK THESE SAMPLES OF Buffron Needle Problem

Peculiarities of Regional and Land Planning

Specifically, the problem of accommodating the skateboarders of LOVE Plaza has been contentious.... A partial plan has been underway to provide solution for the perceived planning problem.... And it cannot be determined whether the problem should be focused on community cohesion, aesthetic, practicality and economy, heritage, safety, or even inclusion.... It should be noted that the problem about inclusion of perceived community “nuisance” in the planning scheme has been a challenge not only for planners but also for policy-makers and the residents....
12 Pages (3000 words) Essay

Netflix & Qwiksters Market Strategy

Reaction to Netflix's strategy to handling the public outcry, success in alleviating the perceived problem, and the organization's image following the attempt to alleviate the perceived problem I believe that Netflix's decision to rescind its initial plans for separating its...
4 Pages (1000 words) Essay

Substance Misuse Treatment

Access to services may be limited based on race or gender, and under-qualified providers may be less than adequate to appropriately deal with the magnitude of the problem. ... It aids the client by introducing them to the programs available and increases their sense of awareness in relationship to their drug problem.... The competency would range from needle exchange programs to offering and administering brief psychological interventions....
4 Pages (1000 words) Essay

Christian Counseling vs. Professional Psychotherapy

This essay, Christian Counseling vs.... Professional Psychotherapy, discusses that counseling has the aim to help individuals to find the solutions to their emotional, moral and psychological problems.... There is the belief that every single person seeks counsel at least several times a year....
16 Pages (4000 words) Essay

Annotated Soap Note

EENT: no problem with hearing or vision.... A fine needle aspiration was conducted to obtain a tissue for testing.... Three months have passed since I saw a doctor after the lumpectomy surgery I underwent.... I want to get married but I need to verify my present status”. ...
3 Pages (750 words) Assignment

Personal Development Planning - Report

Personal development planning is the creation of action plans that are aimed at recording an individual achievement, reflecting on ones learning performance as well as achievement.... It is based on contextualizing ones all round personal, career and education development.... It helps… Second, it helps identify the skills and experiences that one has acquired over a given period and those that one needs to acquire....
5 Pages (1250 words) Assignment

Briefing Note to the Secretary of State for Energy and Climate Change

In light of the climate change patterns and the ever-increasing energy demand in the UK, the UK government is tasked with creating Energy Bills and Legislations that help in the protection of the environment as well as ensuring that the energy needs of the population are met.... hellip; le previous energy bills and legislations have helped in the realization of the above functions, they have not been effective creating a need for the introduction of a new bill that addresses the needs of the market and environmental needs. ...
5 Pages (1250 words) Essay

Accommodating Skateboarders in Balanced Manner at the Plaza Trio Renovation

Specifically, the problem of accommodating the skateboarders of LOVE Plaza has been contentious.... A partial plan has been underway to provide a solution for the perceived planning problem.... And it cannot be determined whether the problem should be focused on community cohesion, aesthetic, practicality, and economy, heritage, safety, or even inclusion.... It should be noted that the problem about inclusion of perceived community “nuisance” in the planning scheme has been a challenge not only for planners but also for policy-makers and the residents....
13 Pages (3250 words) Assignment
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us