Article View: aus.mathematics
Article #181Re: Geometry question.
From: Ken Pledger
Date: Tue, 17 Apr 2007 01:50
Date: Tue, 17 Apr 2007 01:50
37 lines
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3186 bytes
In article <4621e020$0$16555$afc38c87@news.optusnet.com.au>,
"Neil Green" <nrgreenNOSPAM@optusnet.com.au> wrote:
> I need to make some curved rafters for a verandah
> roof.
> The common rafters will be 1500mm when measured in a
> straight line from the end points with a curve of
> 100mm, that is, the mid point of the curve will be
> 100mm from a straight line drawn from end to end, and
> the curve will be part of a circle.
O.K. That much is clear. You could use the technical terms "arc"
(shortened from the Latin word for "bow"), "chord" (from Greek, but
related to the English "cord" meaning a string), and "sagitta" (the
Latin word for "arrow"). A diagram makes the reasons for those names
pretty obvious.
You chord is 1500 mm and your sagitta is 100 mm. Those are enough
to calculate the radius of the circle, which I make 2862.5 mm. (If you
want the formula for that, just ask.)
> I need to know the curve for the rafters at each
> corner of the verandah which are at 45deg.
> The length is obviously 1500mm x sqrt2, but is the
> curve 100mm x sqrt2? ....
That's more obscure. Also, I didn't follow your words "the common
rafters" above. Will you have rafters from left to right, from front to
back, and diagonally as well? Also, your mentioning sqrt(2) suggests
that viewed from above your verandah roof will be square, not just any
old rectangle. I know it's hard without a diagram, but could you
explain in a bit more detail?
Ken Pledger.
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