Fibonacci Sequence Generator

Fibonacci Sequence Generator produces F(0) through F(n) using BigInt arithmetic so precision never degrades. F(100) has 21 digits, F(200) has 42, and every digit is correct. Enter a term count up to 200, choose whether the sequence opens with 0 or 1, and the result appears instantly alongside a visual bar chart and a golden-ratio convergence panel.

The golden-ratio display shows the ratio of the last two consecutive terms and compares it to φ = 1.618033988749895. After just 10 terms the ratio is already within 0.03% of φ; by 20 terms it matches to 6 decimal places. The difference column makes the convergence concrete rather than just claimed.

Worked Example: the First 10 Terms

Press Load Sample and the generator loads 10 terms starting from 0. The sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34

The golden-ratio panel reads F(10)/F(9) = 34/21 = 1.619047…, which already differs from φ by only 0.00101 — less than one tenth of a percent after fewer than a dozen additions.

Switch the Start toggle to 1, 1, 2… and the same 10 positions shift by one: the sequence becomes 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 (F(1) through F(10) in the 1-indexed convention). Both conventions appear in textbooks; the tool copies whichever you chose.

Accuracy and Precision Limits

• All values are exact integers. The generator uses JavaScript BigInt throughout, so there is no floating-point rounding. F(200) = 280571172992510140037611932413038677189525 is stored and displayed without loss. JavaScript’s built-in Number type would start losing precision around F(79).
• The golden-ratio approximation is computed from integers.The ratio F(n)/F(n-1) is calculated by multiplying the numerator by 10¹⁵ and performing integer division, then formatting the result. No floating-point intermediate is involved, so the decimal digits shown are correct to 15 places rather than floating-point-approximated.
• The bar chart shows the first 30 terms only. Later terms grow so fast that a bar sized to include F(200) would make the first 29 bars invisible. The chart is capped at 30; the full sequence is always available via the Copy button.
• At 1 term the sequence is just F(0) = 0. The ratio panel requires at least 2 terms and is hidden when only 1 is requested, because there is no prior term to divide by.

Format Notes

• Copy as CSV produces a comma-separated list on one line — paste directly into a spreadsheet cell or a Python list literal.
• Copy as Lines puts each term on its own line — the format most text processing tools, database imports and competitive programming judges expect.
• The display uses thousands separators for readability. The copied text does not include them, so 1,000,000 in the table copies as 1000000.