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Oh, pi has its place: in engineering, for example, it's much easier to measure the diameter of a pipe than its radius: just put calipers around the widest point
by rmunn 11mo ago
Oh, pi has its place: in engineering, for example, it's much easier to measure the diameter of a pipe than its radius: just put calipers around the widest point (outside or inside depending) and you have the diameter. In fact, you probably wouldn't ever measure the radius; in places where you need the radius, you'd just measure the diameter and divide by 2.
But for teaching trig? Explaining radians should definitely be tau-based.
- cbolton 11mo agoDo you mean the advantage of writing pi*d for the circumference instead of tau*r or tau*d/2? I wouldn't keep pi around just for this...
- rmunn 11mo agoYes, though more broadly my point was that the radius is the natural measurement of the circle for most things since most things are center-based. But for some physical measurements, mostly based around pipes, "what is the width of this pipe" is the question you need answering, and that is diameter-based. And pi is circumference/diameter, while tau is circumference/radius. But yes, if the world switched to tau then you wouldn't need pi anymore, you'd just write tau/2 in the rare cases where having the circumference/diameter ratio handy is useful.