The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem

نویسندگان

  • Jeff Babb
  • James Currie
چکیده

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of results understandable by students without a background in analytic geometry. By a judicious choice of methods and themes, large parts of the history of calculus can be made accessible to students in Humanities or Education.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cuckoo search via Lévy flights for the capacitated vehicle routing problem

For this paper, we explored the implementation of the cuckoo search algorithm applied to the capacitated vehicle routing problem. The cuckoo search algorithm was implemented with Lévy flights with the 2-opt and double-bridge operations, and with 500 iterations for each run. The algorithm was tested on the problem instances from the Augerat benchmark dataset. The algorithm did not perform well o...

متن کامل

An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function

In this paper, an interior-point algorithm  for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...

متن کامل

Contractor selection in MCDM context using fuzzy AHP

Contractor selection is one of the most important problem in supply chain and itsstrongly effect on firm`s performance. Because a significant amount of auniversity`s budget assigns to construction contracts, contractor selection is animportant problem for the financial status of universities. Since Contractor selectionis a multi-criteria decision making problem (MCDM), lots of methods proposed ...

متن کامل

Solving trajectory optimization problems via nonlinear programming: the brachistochrone case study

This note discusses reformulations the brachistochrone problem suitable for solution via NLP. The availability of solvers and modeling languages such as AMPL [1] makes it tempting to formulate discretized optimization problems and get solutions to the discretized versions of trajectory optimization problems. We use the famous brachistochrone problem to warn that the resulting solutions may be f...

متن کامل

Lagrangian Relaxation Method for the Step fixed-charge Transportation Problem

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008