![]() After three months, the first pair will give birth to another pair, resulting in two pairs. At two months, the rabbits have mated but not yet given birth, resulting in only one pair of rabbits. A female rabbit gives birth to one male rabbit and one female rabbit.Īfter one month, the first pair is not yet at sexual maturity and can't mate.After reaching sexual maturity, female rabbits give birth every month.The gestation period of a rabbit is one month.Rabbits reach sexual maturity after one month.Begin with one male rabbit and female rabbit that have just been born.Beginning with a male and female rabbit, how many pairs of rabbits could be born in a year? The problem assumes the following conditions: ![]() Now is this just coïncidence because this pattern assures that each leaf will receive its maximum exposure to sunlight and air without shading or crowding the other leaves.įibonacci first noted the sequence when pondering a mathematical problem about rabbit breeding. In each case the numbers are Fibonacci numbers. This spiral pattern is observed by viewing the stem from directly above, and noting the arc of the stem form one leaf base to the next, and the fraction of the stem circumference which is inscribed. This is the appeal of the golden proportion.Īnother area of great interest is the occurrence of Fibonacci numbers in the spiral arrangement of leaves around a plant's stem (called phyllotaxis). Rather than the effect of stillness and quiet". It gives animation and life to an artist's work. In static symmetry the lines have definite measurements whereas in dynamic symmetry it is the proportioning of the areas that is given emphasis. Why the golden proportion? Art forms can be either of static or dynamic symmetry. Many of the things you use are patterned after the golden rectangle(credit cards, playing cards, postcards, light switch plates, writing pads)Īrtists such as Leonardo da Vinci, Van Gogh, Vermeer, Sargent, Monet, Whistler, Renoir, and others employed the golden proportion in many of their works. The United Nations building is a golden rectangle. This rectangular shape was close to the pattern used in the designing of the Parthenon of Greece and for many of their numerous pictures, vases, doorways, windowns, statues, etc., and even for certain features of the Great Pyramid of Egypt. If the short side of the rectangle is 1, the long side will be 1.618. Why did Greek sculptors, and others in ancient Greece and Egypt often use this ratio in designing many of their works of art? It produces what is called a Golden Rectangle. The higher u go in numbers, the closer the numbers get to the golden ratio (phi) When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio. When the smaller number of this pattern is divided into the larger number next to it, the ratio will be approximately 1.618(phi) if the larger one near to it divides the smaller number, the ratio is very close to 0.618 (=1/ phi). There is a special relationship between the Golden Ratio(phi) and Fibonacci Numbers. This numbering pattern reveals itself in various ways throughout all of nature, as we shall see further in this topic. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. ![]() ![]() They are still called "bougies" in French and Dutch.īy the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the present-day Algerian town of Béjaïa, formerly known as Bugia or Bougie, where wax candles were exported to France. Pisa was an important commercial town in its day and had links with many Mediterranean ports. So he probably merely included the "rabbit problem"(see below) from one of his contacts and did not invent either the problem or the series of numbers which now bear his name. Fibonacci says his book Liber Abaci that he had studied the "nine Indian figures" and their arithmetic as used in various countries around the Mediterranean and wrote about them to make their use more commonly understood in his native Italy. Born in 1175 and commonly assumed to die in 1240. The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa,Italy. ![]()
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