Posted: 9/28/2009 7:58:56 PM EDT
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The minimum number of points that define a unique line is 2. The minimum number of points that define a unique plane is 3. What is the minimum number of points that define a unique arc? Also, what is the minimum number of points that define a unique helix? (or is there?) And what's the formula for each of these? Just some questions that come to mind when I was stuck in traffic today.  |
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Quoted: I would guess 3 points for a unique arc. One at the apex, and two on the "legs." I don't think it has to be the apex. But I agree - probably three. I don't remember enough of my basic math/trig/calc to figure out the formula for this though. And a helix? I'm gonna guess 5, I don't know why. |
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Quoted:
Quoted:
I would guess 3 points for a unique arc. One at the apex, and two on the "legs." I don't think it has to be the apex. But I agree - probably three. I don't remember enough of my basic math/trig/calc to figure out the formula for this though. And a helix? I'm gonna guess 5, I don't know why. No, it doesn't have to be. Just an example. |
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Quoted: Quoted: I would guess 3 points for a unique arc. One at the apex, and two on the "legs." I don't think it has to be the apex. But I agree - probably three. I don't remember enough of my basic math/trig/calc to figure out the formula for this though. And a helix? I'm gonna guess 5, I don't know why. Think about how the question is set up. line - 2 points add a dimension: plane - 3 points arc - 3 points add a dimension: helix - ??? |
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Quoted:
Arc? That would be 3 points. Center, start and end. Note there is an implied radius there. The helix is nothing more than hyperspace of the arc so one more point, the pitch. Not quite true. Any three points in a plane can define a complete circle all of which are in the circumference. Helix,... a planer helix or three dimensional helix? |
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Quoted:
Quoted:
Arc? That would be 3 points. Center, start and end. Note there is an implied radius there. The helix is nothing more than hyperspace of the arc so one more point, the pitch. Not quite true. Any three points in a plane can define a complete circle all of which are in the circumference. Helix,... a planer helix or three dimensional helix? Yep, as long as you have three points on the arc you can find the center point. |