Small challenge
06-07-2017, 09:54 PM
Post: #9
 Pekis Member Posts: 103 Joined: Aug 2014
RE: Small challenge
(06-07-2017 08:42 PM)SlideRule Wrote:  I arrived at a slightly different results:
Δ ≈ 6.52° = interior angle formed by the line segments BOD
(½ the central angle of the sector formed by COD)
θ ≈ 23.58° = interior angle formed by line segments ADO
D ≈ (0.118474, 0.993725)
verified by WolframAlpha & AnalyzeMath
AD ≈ 0.22710 = d = a*R

The difference seems to be associated with the assumption guiding the calculation of the distance EB. I do not see how the Arc Segment S for the sector CAD with a central angle anchored to point A and the Arc Segment for the sector COD with a central angle anchored at point O can both describe the same arc segment CBD.
Although the difference of the sagitta calculated this way may be small, in a manner similar to the small difference between the SIN & the TAN of a small angle, I take exception to the equality of the results, not the equivalency.
Where am I going wrong?

BEST!
SlideRule

Hello,
Don't forget that the points C and D belong to the outer circle with radius r. So, although they also belong to the triangle ACD, the formula I used to calculate the arc height seems perfectly valid. You could imagine a OCD triangle to apply the formula. What do you think ? Thanks
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 Messages In This Thread Small challenge - Pekis - 06-06-2017, 08:05 AM RE: Small challenge - pier4r - 06-06-2017, 01:26 PM RE: Small challenge - Pekis - 06-07-2017, 09:53 AM RE: Small challenge - PedroLeiva - 06-07-2017, 11:35 AM RE: Small challenge - Pekis - 06-07-2017, 03:49 PM RE: Small challenge - PedroLeiva - 06-08-2017, 12:59 PM RE: Small challenge - Jim Horn - 06-07-2017, 04:25 PM RE: Small challenge - Pekis - 06-07-2017, 04:31 PM RE: Small challenge - SlideRule - 06-07-2017, 08:42 PM RE: Small challenge - Pekis - 06-07-2017 09:54 PM RE: Small challenge - SlideRule - 06-07-2017, 10:53 PM RE: Small challenge - Pekis - 06-08-2017, 05:10 AM RE: Small challenge - SlideRule - 06-08-2017, 12:12 PM RE: Small challenge - Vtile - 06-09-2017, 01:14 PM RE: Small challenge - Csaba Tizedes - 06-11-2017, 10:59 AM RE: Small challenge - Pekis - 06-09-2017, 07:08 AM RE: Small challenge - Pekis - 06-11-2017, 09:58 PM

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