One full turn = τ radians
One full revolution = τ radians. τ/4 = 90°. τ/2 = 180° = π radians. The circumference of a circle is C = τr.
τ vs π in common formulas
Comparison of formulas using tau vs pi
| Formel | mit π | mit τ |
|---|---|---|
| Umfang | 2πr | τr |
| Kreisfläche | πr² | τr²/2 |
| Volle Drehung | 2π rad | τ rad |
| Eulers Identität | eⁱπ+1=0 | eⁱτ=1 |
| Gaußsches Integral | √(2π) | √τ |
A quarter turn is τ/4. A half turn is τ/2. A full turn is τ. Intuitive.
With π, a quarter turn is π/2: half of the full-turn constant. With τ, a quarter turn is τ/4: literally one quarter. Every fraction of a turn maps directly to the same fraction of τ.
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Siapa yang mengusulkan penggunaan tau sebagai pengganti pi?
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Hasilkan digit Tau τ
τ has no final digit
Tau τ is irrational. Its decimal expansion never ends and never repeats. The digits shown below are verified against the definisi lingkaran.
τ = 2π = C / r
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