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Pages: 1 2 [>>] | - Page 451 - Section 7.1
The Fibonacci Numbers and Golden section in Nature - 1 -- A variety of ways that Fibonacci numbers arise in nature, including counting rabbits, can be found on Ron Knott's page at the Department of Computing, University of Surrey site.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
(Added: Fri Jul 28 2006)
- Page 451 - Section 7.1
The Fibonacci Numbers and the Golden Section -- A wealth of information about the Fibonacci numbers and the golden mean can be found at the Department of Computing, University of Surrey, site.
http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
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- Page 451 - Section 7.1
Fibonacci Numbers and the Golden Section -- For information about the Fibonacci numbers begin your journey here.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
(Added: Fri Jul 28 2006)
- Page 452 - Section 7.1
Tower of Hanoi Puzzle -- Various algorithms (both recursive and nonrecursive) and interactive Java applets for the Tower of Hanoi puzzle and links to other Tower of Hanoi sites can be found by first going here.
http://hanoitower.mkolar.org/
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- Page 452 - Section 7.1
Tower of Hanoi -- A picture of the 19th century original box cover for the Tower of Hanoi puzzle and the text of the original instructions in French, and translated into English, can be seen at the site of Paul K. Stockmeyer, a professor of computer science at William and Mary College.
http://www.cs.wm.edu/~pkstoc/toh.html
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- Page 452 - Section 7.1
Tower of Hanoi Papers -- Several interesting papers about the Tower of Hanoi problem and its generalizations written by Paul K. Stockmeyer can be downloaded here.
http://www.cs.wm.edu/~pkstoc/h_papers.html
(Added: Fri Jul 28 2006)
- Page 452 - Section 7.1
Tower of Hanoi -- Some history of the Tower of Hanoi problem, animation, and interactive software are available at the Lawrence Hall of Science site.
http://www.lhs.berkeley.edu/Java/Tower/towerhistory.html
(Added: Fri Jul 28 2006)
- Page 452 - Section 7.1
MazeWorks – Tower of Hanoi -- An applet implementing the Tower of Hanoi which runs interactively or automatically can be found here.
http://www.mazeworks.com/hanoi/
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- Page 452 - Section 7.1
Tower of Hanoi on the Web -- A comprehensive list of links to sites devoted to the Tower of Hanoi puzzle can be found here.
http://hanoitower.mkolar.org/HTonWebE.html
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- Page 454 - Section 7.1
Multi-Peg Tower of Hanoi Applet -- This Java applet, developed by Robert J. Swartz, displays solutions to the Tower of Hanoi puzzle using the algorithm that is conjectured to be optimal. The multi-peg version uses an origination peg, a destination peg, and one or more auxiliary pegs; the traditional Tower of Hanoi uses just one auxiliary peg. In this applet, the number of pegs allowed can be any integer from 3 to 50, and the number of disks allowed can be any integer from 3 to 200. Each peg is numbered from left to right.
Using this numbering scheme, you can enter the number of the origination peg, and the number of the destination peg. Furthermore, you can enter the amount of time in milliseconds between the movements of the disks. While the program runs, you can pause the moves, and step through them manually by hitting the "Move 1 Disk" button.
http://www.csie.nctu.edu.tw/~tsaiwn/course/introcs/homework/hwk2002/hanoitower/indexa.html
(Added: Fri Jul 28 2006)
- Page 456 - Section 7.1
Catalan numbers -- An attractive page, part of Robert M. Dickau's Mathematical Figures site, provides illustrations of many of the objects that Catalan numbers count.
http://mathforum.org/advanced/robertd/catalan.html
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- Page 456 - Section 7.1
Eugene Charles Catalan -- You can find a biography of Eugene Charles Catalan here at the MacTutor History of Mathematics site.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Catalan.html
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- Page 456 - Section 7.1
Catalan Numbers -- As mentioned in the text, the Catalan numbers appear as the solution to many different counting problems. A number of the problems can be found here.
http://www-gap.dcs.st-and.ac.uk/~history/Miscellaneous/CatalanNumbers/catalan.html
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- Page 456 - Section 7.1
Catalan's Problem -- Other contributions of Catalan include the Catalan equation and the Fermat-Catalan equation. Descriptions of these problems can be found here.
http://primes.utm.edu/glossary/page.php/CatalansProblem.html
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- Page 457 - Section 7.1 Exercise #12
Census Bureau - POPClocks -- The United States Census Bureau provides a variety of information about population and population growth for the United States and for the world. For information about the current population of the world consult here.
http://www.census.gov/main/www/popclock.html
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- Page 457 - Section 7.1 Exercise #12
World Population Growth Rate: 1950-2050 -- The growth rate of the population of the world is actually projected to decrease. For the latest view, consult here.
http://www.census.gov/ipc/www/img/worldgr.gif
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- Page 457 - Section 7.1 Exercise #16
Amortization Calculator -- You can find an applet written by Bret Whissel that can calculate loan payments, and other quantities, here.
http://ray.met.fsu.edu/~bret/amortize.html
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- Page 459 - Section 7.1 Exercises
Josephus Flavius game -- The Josephus Flavius problem involves a survivor-type game that uses mathematical recursion to determine the winner. A description and solution can be found here.
http://www.cut-the-knot.com/recurrence/flavius.html
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- Page 460 - Section 7.2
Discrete Mathematics Lecture Notes -- The solution of homogeneous and nonhomogeneous recurrence relations is covered in extensive lecture notes written at the University of New England in Armidale, Australia.
http://mcs.une.edu.au/~amth140/Lectures/Lecture_Notes.pdf
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- Page 460 - Section 7.2
Lecture 3 - Recurrence Relations -- A discussion of recurrence relations, including divide-and-conquer recurrence relations, can be found here.
http://www.cs.sunysb.edu/~algorith/lectures-good/node3.html
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- Page 471 - Section 7.2 Exercise #11
The Lucas Numbers -- You can learn more about properties of the Lucas numbers, as well as their connections to the Fibonacci numbers here.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/lucasNbs.html
(Added: Fri Jul 28 2006)
- Page 471 - Section 7.2 Exercise #11
Lucas numbers and the Golden Section -- You can find more information about the Lucas numbers here.
http://milan.milanovic.org/math/english/lucas/lucas.html
(Added: Fri Jul 28 2006)
- Page 474 - Section 7.3
Lecture Notes on Algorithm Analysis and Complexity Theory -- Ian Parberry of University of North Texas provides useful useful material on many topics in discrete mathematics with these lecture notes. You will need a PDF viewer to read these notes.
http://www.eng.unt.edu/ian/books/free/lnoa.pdf
(Added: Fri Jul 28 2006)
- Page 474 - Section 7.3
Lecture 3 - Recurrence Relations -- A discussion of recurrence relations, including divide-and-conquer recurrence relations, can be found here.
http://www.cs.sunysb.edu/~algorith/lectures-good/node3.html
(Added: Fri Jul 28 2006)
- Page 474 - Section 7.3
Divide and Conquer algorithm -- The convex hull of a set of points is the smallest convex set that includes the points. A description of a divide-and-conquer algorithm for finding the convex hull of a set of points and interactive applets can be found here.
http://www.cse.unsw.edu.au/~lambert/java/3d/divideandconquer.html
(Added: Fri Jul 28 2006)
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