What is τ (Tau)?

τ = 2π ≈ 6.28318…
τ ≈ 6.28318530717958647692. Transcendental

τ (tau) is simply 2π. Its advocates argue it is the more natural circle constant: a full revolution is τ radians, a half turn is τ/2 radians, a quarter turn is τ/4. The formula for circumference becomes C = τr (circumference = tau × radius), which is arguably more direct than C = 2πr.

The 'tau manifesto' (Michael Hartl, 2010) argues that many formulas are cleaner with τ. Euler's identity becomes e^(iτ) = 1 (a full rotation returns to start). The area of a circle A = τr²/2 echoes kinetic energy (½mv²) and other quadratic forms.

Whether to use τ or π is largely a matter of convention. Both are transcendental, both are computable, and neither is objectively more fundamental. τ is 6.283185307…

Pi → Euler's Identity →
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