Elipse mathematics?
Elipse mathematics?
Does anyone know how to calculate the widest part of an elipse? I have some formulae for calculating the circumferance and know how to draw one with some string tied to two points. but the radii of the elipse is on either ends of the figure and not in the middle. How do I find it out?
..l.,
If this is for a head band the standard ellipse is not adequate.
Humans heads are not shaped like that.
If this is for your geometry class then the textbook formulas are correct, read no further.
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If it is for a helm head size the front to back and the side to side are the most important dimensions, next to the circumference. Get that right and shape it like a human head and the helm should fit. Remember that often more padding is on the forehead portion.
This allows the nose and faceplate to have better clearance.
Halberds
Humans heads are not shaped like that.
If this is for your geometry class then the textbook formulas are correct, read no further.
____________________________________________________________________
If it is for a helm head size the front to back and the side to side are the most important dimensions, next to the circumference. Get that right and shape it like a human head and the helm should fit. Remember that often more padding is on the forehead portion.
This allows the nose and faceplate to have better clearance.
Halberds
Happy Metal Pounding
- olaf haraldson
- Archive Member
- Posts: 3976
- Joined: Mon Nov 20, 2000 2:01 am
- Location: Canton, NY, USA
Yoshida wrote:I have area=pi*x*y
and perimeter=pi*sqrt of 2(Xsqr+Ysqr)-(X-Y)sqr/2.2
You do realize that that's approximate, right?
I prefer Ramanujan's approximation:
c is about pi(3(a+b)-sqrt((3a+b)(a+3b))
http://en.wikipedia.org/wiki/Circumference
http://home.att.net/~numericana/answer/ellipse.htm#elliptic
Yoshida wrote:If I have a measure of the circumferance, and the length, what's the widest part?
Depends on which approximation of the circumference (perimeter) you've been told is "right."
Since you gave the circumference as
Code: Select all
perimeter=pi*sqrt of 2(Xsqr+Ysqr)-(X-Y)sqr/2.2
Just plug in the circumference(perimeter), and the length (pick X as being the length) and solve for the width (Y).
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P / PI = sqrt( 2(Xsqr + Ysqr) - (X-Y)sqr/2.2 )
(P / PI)sqr = 2(Xsqr + Ysqr) - (X-Y)sqr/2.2
(P / PI)sqr = 2*Xsqr + 2*Ysqr - (Xsqr - 2XY + Ysqr)/2.2
2.2*(P / PI)sqr = 3.4*Xsqr + 2XY + 5.4*Ysqr
Plus in all the known values, and you have a quadratic equation (with Y) to solve for.