Quote:
Originally Posted by Hitchhiker 42
EDIT: Gosh darn I only did those with both points touching the the edges. Lemme work on that.
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Also, don't forget to weight by the number of segments - the x coordinates near the center contain more segments than those near the left and right edges.
In any case, to answer Ether's question, the short answer is "not the same as the average length of segments within a small angle (e.g. 1 second of arc) of vertical within the circle." We've got another build session this evening getting ready for Red Stick Rumble, so I don't know how much I'll get done on this tonight.
Addition:
Hitchhiker, thanks for answering a different question. While walking across the street to get lunch, I think I put some nails in this coffin. Consider these two questions:
- What is the average length of a vertical chord of the unit circle?
- What is the average length of a chord of the unit circle which passes through (-1,0)?
You answered the first - the area of the unit circle divided by its width: pi/2.
I answered the second in my paper a score or so posts back (first problem), in a form that is not incompatible with Ether's method, provided angle is checked before length: 4/pi.
If you answer the second using Ether's method but checking length first, then picking one of two possible angles, you will get an average value of 1.
Completing reducto ad absurdum is left to the reader - back to work!
Quote:
Originally Posted by Ether
I just can't trip you up, can I  |
Well, not that easily.