Apa itu Rasio Emas (φ)?

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The golden division

Fibonacci ratios converge to φ

Table of Fibonacci ratios converging to phi

Pasangan Fib	Rasio	Jarak ke φ
1, 1	1,000	0,618
2, 3	1,500	0,118
8, 13	1,625	0,007
55, 89	1,61818…	0,00015
→ ∞	1,61803…	0

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The golden spiral: each square has a quarter-circle arc forming the nautilus curve

Cut a square from a golden rectangle. The remaining piece is another golden rectangle, smaller by factor 1/φ. Repeat forever. The arc traces the golden spiral seen in shells and galaxies.

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The pentagon: every diagonal is exactly φ times the side

In a regular pentagon with side length 1, every diagonal has length φ ≈ 1.618. The diagonals also divide each other in the golden ratio. Draw all five diagonals and you get a pentagram: itself full of golden proportions.

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Want to test your knowledge?

Question

Apa 10 digit pertama dari phi?

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1 / 10

Hasilkan digit Rasio Emas φ

φ has no final digit

Rasio Emas φ is irrational. Its decimal expansion never ends and never repeats. Every digit shown below is computed from the rumus kuadrat.

φ = (1 + √5) / 2