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Why do you refer to the area? Why not the diameter or the circumference? If you care about the area, why not use the unit circle with area 1? A quarter arc of
by sesqu 15y ago
Why do you refer to the area? Why not the diameter or the circumference? If you care about the area, why not use the unit circle with area 1?
A quarter arc of a circle is π/2 radians, regardless of area.
- MostAwesomeDude 15y ago(To answer your question, the unit circle, with radius one, has area π.) A quarter arc of the unit circle is π/2. A quarter arc of the circle with area 2π, though... Here, let's do it in τ for fun. :3 So, the circle with area τ has radius sqrt(2) (from A = πr^2), diameter 2sqrt(2), and circumference τsqrt(2) (from C = Dπ), thus a quarter arc of that circle is τsqrt(2)/4. That's not a pretty number at all to work with. Maybe keeping the unit circle at its current size is a better idea.
- ianterrell 15y agoA quarter arc of the unit circle is a quarter τ (τ/4). A half arc of the unit circle is a half τ. A 5/19ths arc of the unit circle is 5/19ths τ. How much simpler could it get? Defining the unit circle as a circle with area τ is a contradictory statement and is semantically invalid.