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what is the history of it and how is it different from maclaurin and taylor series
matt grime said:How is bread different from music?
CellarDoor said:Oh, the Parthenon too, but hey, that was one of many achievements set by the Greeks. Those Greeks...
Could you make that more precise? :)matt grime said:It does occur in nature for very good and well understood reasons (it has the 'slowest' converging rational approximation, in a sense that can be made precise)
Eighty said:Could you make that more precise? :)
aeterminator1 said:please give a simple explanation
The Fibonacci series is named after Leonardo Fibonacci, an Italian mathematician who popularized the sequence in his book "Liber Abaci" in the 12th century. However, the sequence was actually discovered by Indian mathematicians centuries before Fibonacci.
The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding numbers, starting with 0 and 1. The Maclaurin series, on the other hand, is a mathematical series used to approximate a function by adding up an infinite number of terms. While the Fibonacci series is a specific sequence of numbers, the Maclaurin series is a general concept used in calculus.
The golden ratio is a mathematical constant that is approximately equal to 1.618. It is often found in nature and has been used in architecture and art. The ratio between consecutive numbers in the Fibonacci series approximates the golden ratio as the sequence progresses, which is why the series is often associated with it.
The Fibonacci series has various applications in mathematics, such as in number theory, geometry, and calculus. It is also used in computer science, finance, and biology. In finance, the series is used in the Fibonacci retracement, a technical analysis tool for predicting potential market trends.
The Taylor series is a mathematical series used to represent a function as an infinite sum of terms. The Maclaurin series is a special case of the Taylor series, where the function is centered at 0. While the Fibonacci series is a specific sequence of numbers, it can be represented by a Taylor series with specific coefficients. However, the two series serve different purposes in mathematics and have different applications.