A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

Surfaces and sequence graphs

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Richard Green
Jan 31, 2026
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The golden ratio, φ=(1+√5)/2, is a famous example of an irrational number, which means that it cannot be expressed exactly as a ratio of two integers. The Kronecker sequence (nφ mod 1) is formed from the numbers (0φ, 1φ, 2φ, 3φ, …) ≈ (0, 1.618, 3.236, 4.854, …) by discarding the part of the number to the left of the decimal point to obtain (0, 0.618, 0.…

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