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Mathematical Laws of Nature: The Factor of Cross-Curricular Connections in Teaching
F0 = 0; F1 = 1; Fn = Fn−1 + Fn−2, n > 1 or
F2 = 1; F3 = 2; F4 = 3 + F5 = 5, F6 = 8 . . .
So, the Fibonacci sequence consists of numbers: 1, 1, 2, 3, 5, 8, 13 . . . .
The sequence given in this way answers the question posed about the
number of pairs of rabbits after one year. Assuming the rabbits live infinitely
long, in 1611 German astronomer Kepler discovered that the ratio of adjacent
sequence members is closer to Φ as n grows, i.e. that:
limn→∞ Fn+1 = Φ
Fn
If we successively construct squares whose sides are equal to the numbers
in the Fibonacci sequence, we get a golden rectangle. If we construct arches
over the diagonals of so constructed squares we get the already mentioned
golden (Fibonacci) spiral (figure 6).
Fibonacci Day is celebrated every year on November 23, or 11/23, as num-
bers 1, 1, 2, 3 make up the beginning of the Fibonacci sequence.
Mathematical Laws of Nature
An example of the problem of Fibonacci rabbits i.e. of getting his sequence
and the value of the golden ratio best reflects the functioning of nature ac-
cording to mathematical rules. The way a great number of plants grow their
trees fully corresponds to the Fibonacci rabbit mating diagram. The best ex-
ample of a golden ratio in nature is the Nautilus shell in which the spiral prin-
ciple of growth is clear (whose growth factor is approximately equal to the
coefficient of the golden ratio). At the cross-section of the shell, chambers
can be seen the animal develops during its growth, flawlessly applying the
mathematical formula (Doczi 2005; Omotehinwa and Ramon 2013).
The appearance of Fibonacci numbers in the plant world is extremely pro-
nounced: from the day of germination, through blossom, to fruit formation.
As the plant grows, the leaves usually develop ‘using’ the Fibonacci num-
bers. The number of petals of most flowers corresponds to the Fibonacci
sequence. The number of plant seeds and their arrangement (arrangement
of apple seeds in its horizontal section) is often related to the Fibonacci se-
quence and the golden ratio (Levitov 1991). The leaves on the plant stem de-
velop to form a spiral around the stem (phillotaxis). If we look at the number
of spiral turns and the number of interspaces between the leaves, we will
notice that for the leaves located in the same direction along the stem (e.g.
leaves no. 1, 4, 9) the following applies: between leaves 1 and 4, the number
283
F0 = 0; F1 = 1; Fn = Fn−1 + Fn−2, n > 1 or
F2 = 1; F3 = 2; F4 = 3 + F5 = 5, F6 = 8 . . .
So, the Fibonacci sequence consists of numbers: 1, 1, 2, 3, 5, 8, 13 . . . .
The sequence given in this way answers the question posed about the
number of pairs of rabbits after one year. Assuming the rabbits live infinitely
long, in 1611 German astronomer Kepler discovered that the ratio of adjacent
sequence members is closer to Φ as n grows, i.e. that:
limn→∞ Fn+1 = Φ
Fn
If we successively construct squares whose sides are equal to the numbers
in the Fibonacci sequence, we get a golden rectangle. If we construct arches
over the diagonals of so constructed squares we get the already mentioned
golden (Fibonacci) spiral (figure 6).
Fibonacci Day is celebrated every year on November 23, or 11/23, as num-
bers 1, 1, 2, 3 make up the beginning of the Fibonacci sequence.
Mathematical Laws of Nature
An example of the problem of Fibonacci rabbits i.e. of getting his sequence
and the value of the golden ratio best reflects the functioning of nature ac-
cording to mathematical rules. The way a great number of plants grow their
trees fully corresponds to the Fibonacci rabbit mating diagram. The best ex-
ample of a golden ratio in nature is the Nautilus shell in which the spiral prin-
ciple of growth is clear (whose growth factor is approximately equal to the
coefficient of the golden ratio). At the cross-section of the shell, chambers
can be seen the animal develops during its growth, flawlessly applying the
mathematical formula (Doczi 2005; Omotehinwa and Ramon 2013).
The appearance of Fibonacci numbers in the plant world is extremely pro-
nounced: from the day of germination, through blossom, to fruit formation.
As the plant grows, the leaves usually develop ‘using’ the Fibonacci num-
bers. The number of petals of most flowers corresponds to the Fibonacci
sequence. The number of plant seeds and their arrangement (arrangement
of apple seeds in its horizontal section) is often related to the Fibonacci se-
quence and the golden ratio (Levitov 1991). The leaves on the plant stem de-
velop to form a spiral around the stem (phillotaxis). If we look at the number
of spiral turns and the number of interspaces between the leaves, we will
notice that for the leaves located in the same direction along the stem (e.g.
leaves no. 1, 4, 9) the following applies: between leaves 1 and 4, the number
283
