Steve Schafer wrote:
x = a - sqrt(a^2 - b^2)
I don't know offhand if there's a straightforward way to arrive at this
result without using trigonometry.
Here you go, though with a slightly different result
(same as Joel Koerwer):
a^2=(b^2)/4+(a-x)^2 (Pythagoras)
solving x: --
x(1,2) = a
Correction
stefan a b = a - a * sqrt (1 - b*b / a*a)
should be:
stefan a b = a - a * sqrt (1 - b*b / (a*a))
*Main stefan 10 8
4.0
(0.01 secs, 524896 bytes)
Thanks
@@i
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On Mon, 27 Aug 2007 19:05:06 +0200, you wrote:
Where do I go wrong (I)?
b is defined to be _half_ of the chord (the semichord, I suppose).
You're assuming it to be the entire chord.
Steve Schafer
Fenestra Technologies Corp.
http://www.fenestra.com/
2007/8/27, Steve Schafer [EMAIL PROTECTED]:
b is defined to be _half_ of the chord (the semichord, I suppose).
You're assuming it to be the entire chord.
Based on the drawing I thought it was the length of the arc (in blue) ?
--
Jedaï
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The author of the question (Tony Morris) actually asked two different
questions, and so people gave two different replies :)
To quote Tony:
"I may have misunderstood his problem (we were drawing in dirt) and actually, it is
the straight line between the two points on the circumference that
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I went camping on the weekend and a friend of mine who is a builder
asked me many questions on geometry as they apply to his every day work
- - most of which I could answer.
However, there was one that I couldn't and I am having trouble googling
a
Hi Tony,
x is called the sagitta. At least when making a telescope mirror it is[1].
By bisecting your angle with another radius, you'll see that you have
a right triangle with hypotenuse a, and legs of length (b/2) and
(a-x). Then
sagitta a b = a - sqrt (a*a - b*b/4)
Considered as a function
You've got a which is the radius of the circle, and b which is the
length of the arc, thus you've got the angle between the two red
radiuses : u = b / a
So with basic trigonometry, we can deduce a - x = a * cos(u/2)
x = a *( cos(u/2) - 1)
--
Jedaï
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On Mon, Aug 27, 2007 at 11:04:58AM +1000, Tony Morris wrote:
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I went camping on the weekend and a friend of mine who is a builder
asked me many questions on geometry as they apply to his every day work
- - most of which I could answer.
2007/8/27, Chaddaï Fouché [EMAIL PROTECTED]:
You've got a which is the radius of the circle, and b which is the
length of the arc, thus you've got the angle between the two red
radiuses : u = b / a
So with basic trigonometry, we can deduce a - x = a * cos(u/2)
x = a *( cos(u/2) - 1)
--
On Mon, 27 Aug 2007 11:04:58 +1000, you wrote:
-BEGIN PGP SIGNED MESSAGE-
Hash: SHA1
I went camping on the weekend and a friend of mine who is a builder
asked me many questions on geometry as they apply to his every day work
- - most of which I could answer.
However, there was one that
On Sun, 26 Aug 2007 21:30:30 -0400, you wrote:
I don't know offhand if there's a straightforward way to arrive at this
result without using trigonometry.
Duh. Of course there is
Steve Schafer
Fenestra Technologies Corp.
http://www.fenestra.com/
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