Page 283 - Volk, Marina, Štemberger, Tina, Sila, Anita, Kovač, Nives. Ur. 2021. Medpredmetno povezovanje: pot do uresničevanja vzgojno-izobraževalnih ciljev. Koper: Založba Univerze na Primorskem
P. 283
Mathematical Laws of Nature: The Factor of Cross-Curricular Connections in Teaching
ab ab
aa
a+b Figure 4 The Golden Spiral
Figure 3 The Golden Rectangle
so is the greater to the less (figure 2), then it may denote the described rela-
tionship, proportion, division, or number.
a = a+b d=ef Φ, a > b > 0.
b a
Φ is obtained as a positive solution of the quadratic equation x2 −x −1 = 0,
and it is an irrational number (Kelley 2012):
Φ= 1+ 2 5
≈ 1,6180339887 . . .
A golden rectangle is a rectangle whose side lengths are in the golden ra-
tio, which is approximately 1 : 1.618 (figure 3).
An interesting feature of the golden rectangle is that that when an in-
scribed square is removed, the remaining rectangle is again golden, mean-
ing its sides meet the same proportion as the starting rectangle sides. Thus
a smaller square can be removed, and so on, with a spiral pattern resulting
(figure 4).
Fibonacci Sequence
Leonardo Pisano Fibonacci published the Book of Calculation (Liber Abaci) in
which he raised and solved the problem involving the growth of a popula-
tion of rabbits. The solution was a sequence of numbers later known as the
Fibonacci sequence. Defining this problem, which at first appears to have
nothing to do with the golden ratio, Fibonacci has significantly expanded
the scope of golden ratio application. At the time the Book of Calculation
was published, only a few more privileged European intellectuals who stud-
ied the translations of Arabic mathematicians’ works were familiar with the
281
ab ab
aa
a+b Figure 4 The Golden Spiral
Figure 3 The Golden Rectangle
so is the greater to the less (figure 2), then it may denote the described rela-
tionship, proportion, division, or number.
a = a+b d=ef Φ, a > b > 0.
b a
Φ is obtained as a positive solution of the quadratic equation x2 −x −1 = 0,
and it is an irrational number (Kelley 2012):
Φ= 1+ 2 5
≈ 1,6180339887 . . .
A golden rectangle is a rectangle whose side lengths are in the golden ra-
tio, which is approximately 1 : 1.618 (figure 3).
An interesting feature of the golden rectangle is that that when an in-
scribed square is removed, the remaining rectangle is again golden, mean-
ing its sides meet the same proportion as the starting rectangle sides. Thus
a smaller square can be removed, and so on, with a spiral pattern resulting
(figure 4).
Fibonacci Sequence
Leonardo Pisano Fibonacci published the Book of Calculation (Liber Abaci) in
which he raised and solved the problem involving the growth of a popula-
tion of rabbits. The solution was a sequence of numbers later known as the
Fibonacci sequence. Defining this problem, which at first appears to have
nothing to do with the golden ratio, Fibonacci has significantly expanded
the scope of golden ratio application. At the time the Book of Calculation
was published, only a few more privileged European intellectuals who stud-
ied the translations of Arabic mathematicians’ works were familiar with the
281
