Fibonacci and the golden ratio
The Fibonacci sequence always sums the two previous terms, and the ratio between consecutive terms converges to a famous irrational number, the golden ratio φ. This page shows that convergence, the real limit the generator enforces, and why plain JavaScript would break this math without BigInt.
With only a few terms, the ratio still misses φ = 1.6180339887... at the 3rd decimal place, though it is already visibly close.
This value no longer fits exactly inside Number.MAX_SAFE_INTEGER (2^53-1 = 9,007,199,254,740,991); the generator stays exact because it sums terms with BigInt, not Number.
500 is the maximum number of terms the generator accepts at once; even with numbers over 100 digits long, the ratio between the last two terms still matches φ to the first 10 decimal places.
It is a sequence of integers where each term is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… It is defined by the recurrence F(n) = F(n−1) + F(n−2), with F(0) = 0 and F(1) = 1. It was popularized by Leonardo of Pisa ('Fibonacci') in the 13th century, in a problem about breeding rabbits.
φ = (1+√5)/2 = 1.6180339887498948..., an irrational number that never ends or repeats; the Fibonacci sequence is just one of the best-known ways to approximate it, and the approximation improves with every added term.
By modern mathematical convention, the sequence starts at F(0)=0 and F(1)=1; some older sources start counting at F(1)=1 and F(2)=1, skipping the initial zero, but the generator follows the zero-indexed convention, so the term at index 10 is F(10)=55.
No: growth-proportion ratios in shell spirals, sunflower seed arrangements and leaf phyllotaxis often approximate the golden ratio, but that is an approximate biological growth pattern, not an exact count of Fibonacci terms.
Because JavaScript's Number type represents integers exactly only up to 2^53-1; starting at F(79), sums using Number would begin rounding and producing slightly wrong terms, so the generator adds terms using BigInt, which has no such ceiling, to keep all 500 terms exact down to the last digit.
First 10 Fibonacci terms
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