Please post your football related Polls in this forum
by RUSHIE#9 » Thu Nov 03, 2005 10:07 pm
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RUSHIE#9
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by woof woof ! » Fri Nov 04, 2005 10:08 am
For the one or two people in here that dont know ,a prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called "spindle-shaped ellipsoid" ). A symmetrical egg (i.e., with the same shape at both ends) would approximate a prolate spheroid. A prolate spheroid is a surface of revolution obtained by rotating an ellipse about its major axis , and has Cartesian equations
(x^2+y^2)/(a^2)+(z^2)/(c^2)==1.
The ellipticity of the prolate spheroid is defined by
e=sqrt((c^2-a^2)/(c^2))==(sqrt(c^2-a^2))/c==sqrt(1-(a^2)/(c^2)).
The surface area of a prolate spheroid can be computed as a surface of revolution about the z-axis,
S==2piintr(z)sqrt(1+[r^'(z)]^2)dz
with radius as a function of z given by
r(z)==asqrt(1-(z/c)^2).
The integrand is then
rsqrt(1+r^('2))==asqrt(1+((a-c)(a+c)z^2)/(c^4)),
and the integral is given by
S = 2piaint_(-c)^csqrt(1+((a-c)(a+c)z^2)/(c^4))dz
= 2pia^2+(2piac^2)/(sqrt(c^2-a^2))sin^(-1)((sqrt(c^2-a^2))/c).
Using the identity
sqrt(c^2-a^2)==ce
gives
S==2pia^2+2pi(ac)/esin^(-1)e
Note that this is the conventional form in which the surface area of a prolate spheroid is written, although it is formally equivalent to the conventional form for the oblate spheroid via the identity
(c^2pi)/(e(a,c))ln[(1+e(a,c))/(1-e(a,c))]==(2piac)/(e(c,a))sin^(-1)[e(c,a)],
where e(x,y) is defined by
e(x,y)=sqrt(1-(x^2)/(y^2)).
Although an interesting idea I personally feel that instead of a prolate spheroid the use of a headless goat would, especially at throw ins, add more comedy value to any game .
Last edited by
woof woof ! on Fri Nov 04, 2005 10:10 am, edited 1 time in total.
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woof woof !
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by andy_g » Fri Nov 04, 2005 6:00 pm
nicely done
Get up! everybody's gonna move their feet
Get Down! everybody's gonna leave their seat
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by Woollyback » Sat Nov 05, 2005 12:37 am
reefer madness
b*ll*c*ks and s*i*e
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by neil » Sat Nov 05, 2005 12:52 am
throw-ins it is then.
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by hawkmoon269 » Sat Nov 05, 2005 1:17 am
woof woof ! wrote:For the one or two people in here that dont know ,a prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called "spindle-shaped ellipsoid" ). A symmetrical egg (i.e., with the same shape at both ends) would approximate a prolate spheroid. A prolate spheroid is a surface of revolution obtained by rotating an ellipse about its major axis , and has Cartesian equations
(x^2+y^2)/(a^2)+(z^2)/(c^2)==1.
The ellipticity of the prolate spheroid is defined by
e=sqrt((c^2-a^2)/(c^2))==(sqrt(c^2-a^2))/c==sqrt(1-(a^2)/(c^2)).
The surface area of a prolate spheroid can be computed as a surface of revolution about the z-axis,
S==2piintr(z)sqrt(1+[r^'(z)]^2)dz
with radius as a function of z given by
r(z)==asqrt(1-(z/c)^2).
The integrand is then
rsqrt(1+r^('2))==asqrt(1+((a-c)(a+c)z^2)/(c^4)),
and the integral is given by
S = 2piaint_(-c)^csqrt(1+((a-c)(a+c)z^2)/(c^4))dz
= 2pia^2+(2piac^2)/(sqrt(c^2-a^2))sin^(-1)((sqrt(c^2-a^2))/c).
Using the identity
sqrt(c^2-a^2)==ce
gives
S==2pia^2+2pi(ac)/esin^(-1)e
Note that this is the conventional form in which the surface area of a prolate spheroid is written, although it is formally equivalent to the conventional form for the oblate spheroid via the identity
(c^2pi)/(e(a,c))ln[(1+e(a,c))/(1-e(a,c))]==(2piac)/(e(c,a))sin^(-1)[e(c,a)],
where e(x,y) is defined by
e(x,y)=sqrt(1-(x^2)/(y^2)).
Although an interesting idea I personally feel that instead of a prolate spheroid the use of a headless goat would, especially at throw ins, add more comedy value to any game .
What's wrong with using a rugby ball - it's worked in the past?
We just need to get used to the idea!
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by woof woof ! » Sat Nov 05, 2005 4:31 am
hawkmoon269 wrote:What's wrong with using a rugby ball - it's worked in the past?
Yeah , until some clever fk picks it up an runs with it .
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by The Canadian Red Army » Tue Nov 08, 2005 5:45 pm
andy_g wrote:to me its ridiculous that outfield players are allowed to use their hands for a throw in, the rules should remain consistent and forbid it. that would leave us with only the goalkeeper able to take throw ins which is obviously a bit stupid.
therefore i would favour the head in. the player has to place the ball on the deck, take a run up and launch himself at it, trying to get as much distance as possible with a diving header.
hahaha i just read this now, thanks for the laugh andy
RIP - Drummerphil - YNWA
" Whats a holly kipper CRA? Is that a scene from batman and Robin
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This is soo true - Daniel - sweetest guy in the world,soft and gentle but good in bed! hes a keeper!!!!!!
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by neil » Thu Nov 10, 2005 12:42 am
you look as though your just the man for the job.
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Lando_Griffin
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by Judge » Thu Nov 10, 2005 9:05 am
andy_g wrote:to me its ridiculous that outfield players are allowed to use their hands for a throw in, the rules should remain consistent and forbid it. that would leave us with only the goalkeeper able to take throw ins which is obviously a bit stupid.
therefore i would favour the head in. the player has to place the ball on the deck, take a run up and launch himself at it, trying to get as much distance as possible with a diving header.
thats a fantastic idea
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