Assignment 6a: Algorism
Due:
-Annandale- Tuesday, March 5^{th}
-Fishkill- Wednesday, March 13^{th}
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:
RadioLab-For
the Love of Numbers
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