Assignment 6a: Algorism

Due:

-Annandale- Tuesday, March 5th

-Fishkill- Wednesday, March 13th Read the following: folios Fibonacci [Leonardo Pisano, Leonardo of Pisa (ca. 1170-ca. 1250)].  Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation.  (First appeared in 1202.) Translation and Notes by Laurence Sigler.  Springer. 2002. Excerpts. pp. 3-11: Introduction by Sigler pp. 15-16: Prologue to Liber abaci pp. 17-22: Chapter 1 4 Suzuki, Jeff. Mathematics in Historical Context. Mathematical Association of America. 2009. pp. 122-124: Leonardo of Pisa (Fibonacci) 1 Struik, Dirk Jan, ed.  A Source Book in Mathematics, 1200-1800.  Source Books in the History of the Sciences. Cambridge, Mass.,: Harvard University Press, 1969. pp. 1-4: Arithmetic: Leonardo of Pisa (Fibonacci): The Rabbit Problem 1 Chuquet, Nicolas, Graham Flegg, Cynthia Hay, and Barbara Moss.  Nicolas Chuquet, Renaissance Mathematician: A study with extensive translation of Chuquet's mathematical manuscript completed in 1484.  Boston.  D. Reidel Publishing.  1985.  Excerpts. pp. 27-29: numeration 1

HW-6a

1)  Fibonacci's Rabbit Problem is one of the most famous in mathematics.  The sequence of Fibonacci numbers (or the Fibonacci Sequence) is easy to do abstractly, but the whole story about rabbit population dynamics is a bit more difficult to grasp.  In the diagram at the top of this page I have worked out a systematic way to express the rabbit problem, but I only did it up to 8 pairs.  You need to read the excerpt from Fibonacci's Liber abaci (in the Struik reading), figure it out, and figure out my diagram.  E.g. What is meant by b and A?  What are the arrows?  What are the numbers?  Your task is to make a diagram that goes all the way to 21.  [1, 1, 2, 3, 5, 8, 13, 21.]  Include any notes or comments that might help me understand your method.

Topical Podcasts:

Notes to self....

Chuquet, pp. 27-29: Numeration.  He also deals with really big numbers in a special way.

pp. 43-59?  Reducing fractions, series, and perfect numbers

Grant: Sacrobosco, ch20, pp. 94-101