Leonardo Pisano Bigollo

Definition. Similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a Fibonacci integer sequence. The first two Lucas numbers are L0 = 2 and L1 = 1 as opposed to the first two Fibonacci numbers F0 = 0 and F1 = 1.

Fibonacci sequence

Leonardo of Pisa is now known as Fibonacci [pronounced fib-on-arch-ee] short for filius Bonacci. Fibonacci is a shortening of the Latin “filius Bonacci”, used in the title of his book Libar Abaci (of which mmore later), which means “the son of Bonaccio”. His father’s name was Guglielmo Bonaccio.

Leonardo Fibonacci discovered the sequence which converges on phi. He is also known as Leonardo Bonacci, as his name is derived in Italian from words meaning “son of (the) Bonacci”. Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.

We observe that many of the natural things follow the Fibonacci sequence. It appears in biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone’s bracts etc.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811.

6,765

In general, pineapples have three series of spirals, derived from the roughly hexagonal pattern of its fruitlets, or scales. Here is an example of the hexagonal scale patterns found on a pineapple.

The golden ratio is about 1.618, and represented by the Greek letter phi, Φ. The golden ratio is best approximated by the famous “Fibonacci numbers.” Fibonacci numbers are a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers.

Mathematics, physics and chemistry can explain patterns in nature at different levels. Patterns in living things are explained by the biological processes of natural selection and sexual selection. Studies of pattern formation make use of computer models to simulate a wide range of patterns.

A few examples include the number of spirals in a pine cone, pineapple or seeds in a sunflower, or the number of petals on a flower. The numbers in this sequence also form a a unique shape known as a Fibonacci spiral, which again, we see in nature in the form of shells and the shape of hurricanes.

The mathematical ideas the Fibonacci sequence leads to, such as the golden ratio, spirals and self- similar curves, have long been appreciated for their charm and beauty, but no one can really explain why they are echoed so clearly in the world of art and nature. The story began in Pisa, Italy in the year 1202.

Fibonacci is famous for his contributions to number theory. In his book, “Liber Abaci,” he introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. He introduced the bar that is used for fractions today; previous to this, the numerator had quotations around it.

The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

Leonardo of Pisa

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.