Mathematical Calculators
Fibonacci Calculator
This Fibonacci calculator can be used to calculate the terms arbitrarily of the Fibonacci sequence.
Fibonacci Calculator
Table of contents
| ◦What is the Fibonacci sequence and how does it work? |
| ◦Formula for the n-th term |
| ◦The Golden Ratio |
What is the Fibonacci sequence and how does it work?
Fibonacci sequence refers to a series of numbers that follows a specific rule: Each term in the sequence must equal the sum of the two preceding terms. Each term can be expressed using this equation:
բₙ ₌ բₙ₋₂ ₊ բₙ₋₁
Fibonacci sequences typically have F0 = 0, F1 = 1, and F2 = 1. You can also choose F1 = 1, or F2 = 1 to start the sequence. You will need at least two terms consecutively to solve the arithmetic series.
Negative terms can also be covered by the Fibonacci sequence rule. For example, F-1 can be found to be equal to 1.
The Fibonacci sequence's first 15 terms are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
Fibonacci numbers are interestingly consistent with the well-known Benford’s law.
Formula for the n-th term
The good news is that you don't need to calculate all the preceding terms in order to calculate the next term of a sequence. You can find an arbitrary term in a sequence with a simple formula:
բₙ ₌ ₍φⁿ ₋ ψⁿ₎ / √₅
բₙ: the n-th term of the sequence
φ: golden ration equal to (1 + √5)/2, or 1.618...)
The Fibonacci Sequence is a sequence of numbers.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
You can find the next number by adding up both numbers before it.
Here's a more extensive list:
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, ...
| n = | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | ... |
| xn = | 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | ... |
The Golden Ratio
The gold ratio " is a unique mathematical relationship. Two numbers can be considered to be in the "golden ratio" if the proportion of both the numbers (a+b), and the larger number (a), is equal to that of the larger number and the smaller number (a/b). The golden ratio can be represented by the Greek letter "phi", φ.
The Fibonacci Number best describes the golden ratio. Fibonacci number are a never ending sequence that begins with 1 and goes on to add the next two numbers. The next numbers in Fibonacci's sequence are, for example, 1,2,3, and 5.
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Parmis Kazemi
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Fibonacci Calculator English
Published: Tue Mar 08 2022
In category Mathematical calculators
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