Maths loves nature and‌ ‌nature loves spirals
What they have in common the galaxy, the biological growth of some species of animals and plants, the spacing between the leaves, the arrangement of petals and seeds of a sunflower? All of these have pattern that can be traced back to that of golden section and the numbers of Fibonacci.
Here is a series of images in which the mathematical expression manifests itself in the beauty and elegance of nature
Roman gabbage
snail
web
Sea snail
Fat plant The common element to all the figures is the logarithmic spiral called “golden spiral�or of growth, through which the harmonious development of form is linked to the necessity of living beings to increase "second nature" in the best and least expensive way possible.
A little bit of spiral history Galileo Galilei asserted that the harmony of the world manifests itself in form and numbers. The logarithmic spiral was first studied in 1638 by RenĂŠ Descartes (1596-1650): "(...) is called a logarithmic spiral every flat figure that proceeds from a fixed point such that the area vector of any section is always an added proportion of the previous figure. " The Swiss mathematician Jakob Bernoulli (1654 - 1705) defined the "Spira mirabilis" curve, the spiral marvelous, assuming that it was carved on his grave next to the phrase "Eadem mutated resurgence ", that is" although different, I renounce equally ". As far as tombstone is concerned, unfortunately the stonecutter engraved a spiral of Archimedes.
Curiosity Among the spiral studies, mention should be made of the ancient Greek Mathematical Theodore of Cyrene from a Pythagorean school (which we studied in the past few months). • Here is a geogebra construction (geometry program for secondary schools).
1. 2. 3. 4.
It starts from the ABCD square of the unit side Track the diagonal of the square that is long √2 Track segment ED = 1 perpendicular to diagonal BD. EB = √ (2 + 1) = √3 It traces the FE = 1 perpendicular to BE. FB = √ (3 + 1) = √4 = 25. And so on ... This Theodore is hot, is not it? Going forward.
Be careful not to confuse! By the name Theodore of Cirene are indicated: • Theodore of Cirene (dead in 310) - bishop and holy martyr, celebrated on 4 July • Theodore of Cirene (IV-III century BC) - said "the atheist", exponent of the Cirenaic School • Theodore of Cyrene (5th century BC) - mathematician of the Pythagorean School Our Theodore was an ancient Greek mathematician, known for his contribution to the theory of irrational magnitudes, he was part of the Pythagorean School.
Works in class with geogebra.
In this work it has been reproduced the growth of a Nautilus with geogebra software.
Study in nature