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The circumference of a circle is π times its diameter, so C = πd (equivalently, C = 2πr, where r is the radius). Thus the ratio of circumference to diameter is constant, π (≈ 3.14159).
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Yes — that's correct.
Reason: All circles are similar, so circumference is proportional to diameter: C = k·d for some constant k. That constant is defined as π, so C = πd (equivalently C = 2πr). Numerically π ≈ 3.141592653589793..., it is irrational (non‑repeating, non‑terminating) and transcendental (not a root of any nonzero polynomial with integer coefficients).
Related formulas:
- Area: A = πr^2
- Arc length for central angle θ (radians): s = rθ
- Sector area for angle θ (radians): A_sector = 1/2 r^2 θ
Would you like a short proof sketch that circumference is proportional to diameter, or more about π’s properties or history?
Reason: All circles are similar, so circumference is proportional to diameter: C = k·d for some constant k. That constant is defined as π, so C = πd (equivalently C = 2πr). Numerically π ≈ 3.141592653589793..., it is irrational (non‑repeating, non‑terminating) and transcendental (not a root of any nonzero polynomial with integer coefficients).
Related formulas:
- Area: A = πr^2
- Arc length for central angle θ (radians): s = rθ
- Sector area for angle θ (radians): A_sector = 1/2 r^2 θ
Would you like a short proof sketch that circumference is proportional to diameter, or more about π’s properties or history?
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