Page 284 - Volk, Marina, Štemberger, Tina, Sila, Anita, Kovač, Nives. Ur. 2021. Medpredmetno povezovanje: pot do uresničevanja vzgojno-izobraževalnih ciljev. Koper: Založba Univerze na Primorskem
P. 284
gica Milinković, Milenko Ćurčić, and Slađana Mitrović
Figure 5 Fibonacci Rabbits 5
8
11
3
2
Figure 6 Fibonacci Spiral
Hindu-Arabic numbers we use today. The Fibonacci sequence was known to
Indian mathematicians as early as in the sixth century, and Fibonacci brought
it closer to Europe.
The original problem studied by Fibonacci in 1202 was about how fast rab-
bits could breed in ideal circumstances. Suppose a newly-born pair of rabbits,
a male and a female, are put in a field and rabbits are able to mate at the age
of one month so that at the end of its second month a female can produce
another pair of rabbits. Suppose our rabbits never die and that the female
always produces one new pair (one male and one female) every month from
the second month on. The question that Fibonacci posed was: How many
pairs will there be in one year? At the end of the first month, rabbits mate,
but there is still one only 1 pair. At the end of the second month, the female
produces a new pair, so now there are 2 pairs of rabbits in the field (of which 1
pair is capable of further reproduction next month and 1 is not). At the end of
the third month, the original female produces a second pair, making 3 pairs
of rabbits in the field (of which 2 pairs are capable of further reproduction
next month and 1 is not). At the end of the fourth month, the original female
has produced another new pair, the female born two months ago produces
her first pair also, making 5 pairs of rabbits (of which 3 pairs are capable of fur-
ther reproduction next month and 2 are not) . . .. So, the number of rabbits at
the beginning of the month will be: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,
610, 987 . . . . The number of pairs of rabbits in a given month is equal to the
sum of the number of pairs of rabbits from the previous two months (figure
5) (Koshy 2001; Lučić 2009; Milojković 2009).
About 400 years after Fibonacci, Kepler explicitly wrote what Fibonacci had
surely noticed, that we can define the Fibonacci sequence as follows:
282
Figure 5 Fibonacci Rabbits 5
8
11
3
2
Figure 6 Fibonacci Spiral
Hindu-Arabic numbers we use today. The Fibonacci sequence was known to
Indian mathematicians as early as in the sixth century, and Fibonacci brought
it closer to Europe.
The original problem studied by Fibonacci in 1202 was about how fast rab-
bits could breed in ideal circumstances. Suppose a newly-born pair of rabbits,
a male and a female, are put in a field and rabbits are able to mate at the age
of one month so that at the end of its second month a female can produce
another pair of rabbits. Suppose our rabbits never die and that the female
always produces one new pair (one male and one female) every month from
the second month on. The question that Fibonacci posed was: How many
pairs will there be in one year? At the end of the first month, rabbits mate,
but there is still one only 1 pair. At the end of the second month, the female
produces a new pair, so now there are 2 pairs of rabbits in the field (of which 1
pair is capable of further reproduction next month and 1 is not). At the end of
the third month, the original female produces a second pair, making 3 pairs
of rabbits in the field (of which 2 pairs are capable of further reproduction
next month and 1 is not). At the end of the fourth month, the original female
has produced another new pair, the female born two months ago produces
her first pair also, making 5 pairs of rabbits (of which 3 pairs are capable of fur-
ther reproduction next month and 2 are not) . . .. So, the number of rabbits at
the beginning of the month will be: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,
610, 987 . . . . The number of pairs of rabbits in a given month is equal to the
sum of the number of pairs of rabbits from the previous two months (figure
5) (Koshy 2001; Lučić 2009; Milojković 2009).
About 400 years after Fibonacci, Kepler explicitly wrote what Fibonacci had
surely noticed, that we can define the Fibonacci sequence as follows:
282
