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\fs24\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\f1\fs44\insrsid4537022 Zackary Karas
\par Period: 4
\par 5-29-06
\par }\pard \qc \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 {\f1\fs96\insrsid4537022 Fibonacci
\par }{\f1\fs40\insrsid4537022 1720-1250
\par 
\par }\pard \ql \li0\ri0\nowidctlpar\faauto\rin0\lin0\itap0 {\f1\insrsid4537022 \tab }{\insrsid4537022 
\par }\pard \ql \li0\ri0\sb100\sa100\sl480\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid4537022 {\insrsid4537022 \tab Leonardo Pisano is better known by his nickname Fibonacci}{\b\insrsid4537022 .}{\insrsid4537022 
 He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. 
\par \tab Fibonacci was born in Italy, but
 wasnt educated there. He was educated in North Africa while his father, Guilielmo was on duty. His father represented the merchents of the Republic of Pisa. They traded in Bugia which later on would be called Bougie but now is called Bejaia. Fibonacci wa
s taught mathematics in Bejaia and realized the importance of it.
\par \tab During 1200 he returned to Pisa and wrote his mathematics in a book but he had to make several copies and back then the only way to do that is hand-written each individual copy. We today hav
e most of his books but some got lost due to the years. He wrote very abstract theorems that have made him famous. But today there is a famous theorem called the Fibonacci numbers. He best remembered for this-  "}{\i\insrsid4537022 
A certain man put a pair of rabbits in a pla
ce surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?". the ending results are: }{
\insrsid4537022 1, 1, 2, 3,
 5, 8, 13, 21, 34, 55, ... (Add the last two together to get the next number). These will keep going forever into infinity. Other works of his are- A spider climbs so many feet up a wall each day and slips back a fixed number each night, how many days doe
s it take him to climb the wall.\line A hound whose speed increases arithmetically chases a hare whose speed also increases arithmetically, how far do they travel before the hound catches the hare.\line 
Calculate the amount of money two people have after a certain amount changes hands and the proportional increase and decrease are given. Fibonacci treats numbers such as \u8730\'76
10 in the fourth section, both with rational approximations and with geometric constructions. 
\par }\pard \qj \li0\ri0\sb100\sa100\sl480\slmult1\nowidctlpar\faauto\rin0\lin0\itap0\pararsid4537022 {\insrsid4537022 \tab But wait there is more some other of his writing is: there is no }{\i\insrsid4537022 x}{\insrsid4537022 , }{\i\insrsid4537022 y}{
\insrsid4537022  such that }{\i\insrsid4537022 x}{\super\insrsid4537022 2}{\insrsid4537022  + }{\i\insrsid4537022 y}{\super\insrsid4537022 2}{\insrsid4537022  and }{\i\insrsid4537022 x}{\super\insrsid4537022 2}{\insrsid4537022  - }{\i\insrsid4537022 y}{
\super\insrsid4537022 2}{\insrsid4537022  are both squares. 
\par and }{\i\insrsid4537022 x}{\super\insrsid4537022 4}{\insrsid4537022  - }{\i\insrsid4537022 y}{\super\insrsid4537022 4}{\insrsid4537022  cannot be a square.\line \tab 
\par }\pard \qj \li0\ri0\sb100\sa100\nowidctlpar\faauto\rin0\lin0\itap0 {\insrsid4537022 \tab 
\par }\pard \ql \li0\ri0\sb100\sa100\nowidctlpar\faauto\rin0\lin0\itap0 {\insrsid4537022 
\par 
\par 
\par 
\par 
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\par }}