Transcript Fibonacci - Central High School

Fibonacci
By Andréa Rivard
Leonardo Fibonacci
• Born in Italy c.1170
• Arabic numerals, algorithms
and algebraic methods, and
a facility in fractions
• Fibonacci Sequence
▫ Discovered it by studying
rabbit regeneration
http://www.nndb.com/people/922/000095637/fibonacci-2.jpg
More on Fibonacci
• Grew up in North Africa
• Published the book Liber Abaci
▫ Fun fact! Liber Abaci means the book of abacus but the
book has nothing to do with the abacus
• This problem was featured in his book:
Beginning with a single pair of rabbits (one male and one female),
how many pairs of rabbits will be born in a year, assuming that
every month each male and female rabbit gives birth to a new pair
of rabbits, and the new pair of rabbits itself starts giving birth to
additional pairs of rabbits after the first month of their birth?
The Fibonacci Sequence
• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
• Each number is a sum of the two numbers preceding
it
• Appears throughout the “biological realm”, music, etc
http://www.murderousmaths.co.uk/books/pix/cmm803.gif
The Rabbits
• Each number is a sum of the two
previous numbers because the
number of rabbit pairs in a
previous generation plus all of the
newborn pairs is equal to all of
the rabbits who are more than
two months old
• Fibonacci’s rabbits never die
http://www.quabbinqualitypetsupplies.com/sitebuilderco
ntent/sitebuilderpictures/rabbits.jpg
Fibonacci Spiral
• The spiral appears in nature, often in the way leaves
grow or the way seeds grow
• They usually have consecutive Fibonacci numbers
▫ 8 clockwise, 13 counter-clockwise, 13 counterclockwise, 21 clockwise, etc.
• Minimize space and energy uses
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/coneflower.
jpg
http://farm1.static.flickr.com/17/91546600_4b65896f0a.
jpg?v=0
www.googolpower.com
http://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Mammil
aria_gigantea.jpg/757px-Mammilaria_gigantea.jpg
http://farm4.static.flickr.com/3094/2736846377_ed43bfdf
a0.jpg?v=0
Variations on the Fibonacci
Sequence
• Can start with any number, as long as it follows the
pattern
▫ 3, 3, 6, 9, 15, 24……Fibonacci sequence
▫ .1, .1, .2, .3, .5, .8……Fibonacci sequence
“Fibs”
• Poems that follow the sequence
• Six lines
• Created by Greg Pincus
• Example:
One
Small
Precise,
Poetic,
Spiraling mixture
Math plus poetry yields the Fib
Works Cited
• "Leonardo Fibonacci." Columbia Encyclopedia. EBSCOhost.
Grand Junction, CO. Central
High School.18 May 2009
<http://web.ebscohost.com/src/>.
• Choi, Charles Q. "Fibonacci Fandango." Scientific American
EBSCOhost. Central High
School, Grand Junction, CO. 18
May 2009 <http://search.ebscohost.com/login.aspx?>.
• Entin, Carli. "We're Not Fibbing!" Scholastic Math EBSCOhost.
Central High School, Grand
Juncion, CO. 18 May 2009
<http://search.ebscohost.com/login.aspx?>.
• "The (Fabulous) Fibonacci Numbers." Science News EBSCOhost. Central High School, Grand
Junction, CO. 18 May 2009 <http://search.ebscohost.com/login.aspx?>.
• Fibonacci sequence.
• Gale Encyclopedia of Science. Ed. K. Lee Lerner and Brenda Wilmoth Lerner. 4th ed. Detroit: Gale
Group, 2008.
• Scott, Kim. "Fibonacci's World." Discover Apr. 2007: EBSCOhost. Central High School, Grand
Junction, CO. 19 May 2009 <http://search.ebscohost.com/login.aspx?>.
• "Do Plants Know Math?" USA Today Magazine June 2003: EBSCOhost. Central High School, Grand
Junction, CO. 19 May 2009 <http://search.ebscohost.com/login.aspx?>.