The beauty of Mathematics (Fibonacci
sequence)
Department of Mathematics
• Background:
The Fibonacci sequence is named after Leonardo
Pisano (commonly known as Fibonacci), an Italian mathematician who lived from
1170 t01250. By assuming that a newly born breeding pair of rabbits is placed
in a field, that each breeding pair mates at the age of one month, and that by
the end of their second month, they always produce another pair of rabbits, and
that rabbits never die but instead continue to breed forever, Fibonacci
examines the growth of an idealised (biologically unrealistic) population of rabbits.
How many pairs are there going to be in a year? This is the puzzle put forward
by Fibonacci.
•
At the end of the first month,
they mate, but there is still only 1 pair.
•
At the end of the second month
they produce a new pair, so there are 2 pairs in the field.
•
At the end of the third month,
the original pair produce a second pair, but the second pair only mate to
gestate for a month, so there are 3 pairs in all.
•
At the end of the fourth month,
the original pair has produced yet another new pair, and the pair born two
months ago also produces their first pair, making 5 pairs.
•
Introduction:
A series of continuously increasing numbers comes
after a zero at the beginning of the Fibonacci sequence, which is made up of a
set of integers known as the Fibonacci numbers. Every number in the series is
equal to the sum of the two numbers that came before it.
The first 14 integers in the Fibonacci sequence are
as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233.........
It is possible to compute the Fibonacci sequence
mathematically. According to this method, every sequence number is regarded as
a term, denoted by the expression Fn. The number's position in the
series, starting at zero, is indicated by the n. Beginning with n is greater
than or equal to two. As an illustration, the seventh period is referred to as
F6, and the sixth term is called F5.
F0 = 0 (only relevant for the initial
integer)
F1 = 1, which only holds true for the
second integer
Fn = Fn-1 + Fn-2
(which holds true for all other integers)
•
Fibonacci
number in Nature:
We can see an abundance of patterns in nature
thanks to mathematics, which is beautiful. A flower's petal count corresponds
to the Fibonacci number. Fruit and plants. Many flowers have a Fibonacci number
of petals: daisies can have 34, 55, or even 89 petals, while buttercups have
five, lilies and iris have three, some delphiniums have eight, maize marigolds
have thirteen, and some asters have twenty-one.
•
Golden
Ratio:
Any Fibonacci number can be divided by the
preceding one to obtain a ratio of 1.6. The outcome is nearly the same for each
Fibonacci number. Fibonacci numbers such as 144/89, 55/34, and 34/21 will all
approximately correspond to 1.6. The ratio is called the golden ratio.
Distance between fingertip and
elbow/distance between wrist and elbow is equal to Golden Ratio -
•
Conclusion:
It
demonstrates that mathematics is not limited as it currently is. We can
undoubtedly get remarkable outcomes if we attempt to investigate mathematics in
nature. I discovered some fascinating fact number systems, like the Fibonacci
number, here.
•
Reference:
•
Meisner, Gary B. The Golden Ratio: The Divine
Beauty of Mathematics. Race Point Publishing. 2018
•
https://medium.com/@akarsh.sharma/the-magic-of-fibonacci-numbers-f428b5728034
 by Prakash Bayalkoti){kind=link}
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