Thread: Surface Area of a Sphere

I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



Well, it equals , but maybe it's meaningless.

The most commonly seen integral that's meaningful is , where the area element is a strip of the sphere.

if i remember correctly pir^2 integrated
is the volume of a sector of a sphere (pir^3)/3
4 times this is the total volume of the sphere 4/3pir^3
which when diffentiated gives 4pir^2 its surface area

Feel free to ignore Fiveways. He's not exactly an authority on maths, nor particularly coherent.

Originally Posted by fiveworlds

if i remember correctly pir^2 integratedis the area of a sector of a sphere (pir^3)/34 times this is the total area for the sphere 4/3pir^3which when differentiated gives 4pir^2

You do realize that I am talking about the surface area, not the volume. is what you are talking about.

you do realise that 4pir^2 is the surface area and an area is a specific amount of space so i am not incorrect to call it area instead of volume sadly i have never called myself the authority on maths nor would i call it one of my goals for somebody to view me as such i certainly dont want to be

Originally Posted by fiveworlds

an area is a specific amount of space

No it's not.

i am not incorrect to call it area instead of volume

You are actually.
Each of those terms has a specific definite meaning. They are not interchangeable.

Surface area = the amount of surface.
Volume = the amount contained inside the surface.

yet you really dont know the meaning of it obviously. Ps wise man you dont use newtons formula here the only time you would need it is for finding pi so you are incorrect in its application. Note how sombody took the time to write surface in front of area...

Okay, fiveworlds, what you said in post #2 goes like this:

This is nothing more than a curious set of statements ending with the expression for the surface area of a sphere. You didn’t answer the OP’s question, namely what is the geometrical interpretation of the integral .

Originally Posted by Nehushtan

Okay, fiveworlds, what you said in post #2 goes like this:

This is nothing more than a curious set of statements ending with the expression for the surface area of a sphere. You didn’t answer the OP’s question, namely what is the geometrical interpretation of the integral .

Right. My question is whether has a geometric meaning or is it a curious set of statements ending with the expression for the surface area of a sphere, as Nehushtan said.

fiveworlds, what you said is that the derivative of the volume is equal to the surface area of a sphere... that doesn't mean anything, not that I can think of.

Sphere - Wikipedia, the free encyclopedia

Originally Posted by fiveworlds

yet you really dont know the meaning of it obviously. Ps wise man you dont use newtons formula here the only time you would need it is for finding pi so you are incorrect in its application. Note how sombody took the time to write surface in front of area...

#1 Can you use proper grammar? I find it hard to read your post.
#2 What did I do wrong? Which part?

Originally Posted by fiveworlds

Sphere - Wikipedia, the free encyclopedia

You never reasoned your proof, or gave us that link in the first place. And besides, as I said, that doesn't answer me question.

Though I thank you this proof, I never saw it before. Next time be sure to give us a full proof or a link to one instead of making claim out of no where.

Originally Posted by Wise Man

I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



Well, it equals , but maybe it's meaningless.

May I ask where you got the integral from? Your question got me intrigued; I’ve been searching everywhere for an answer without success. I wondered if it might have something to do with solid angles, but apparently not (plus I can’t make out why the limits should be 0 and 2R).

Originally Posted by SpeedFreek

Surface area = the amount of surface.
Volume = the amount contained inside the surface.

Reminds me of the terminology used by my then-teenaged Nephews when relating tales of their experiences with girl friends: they managed to "get some surface".......

jocular

Originally Posted by Nehushtan

Originally Posted by Wise Man

I was wondering if there was any geometric meaning to this integral/area element... what does it mean on a sphere? A very small circle, when added up (0 to 2R), the area is that of the sphere's surface area?



Well, it equals , but maybe it's meaningless.

May I ask where you got the integral from? Your question got me intrigued; I’ve been searching everywhere for an answer without success. I wondered if it might have something to do with solid angles, but apparently not (plus I can’t make out why the limits should be 0 and 2R).

Well, it was really something I came up with ... I'm trying to see if it corresponds to some geometric shape.

It seems that the area element is a small circle, with a radius of , and the area adds up to 2R...hmm... I think it doesn't make sense.

Ah, okay.

To find the surface area of a sphere by summing areas of elements on the surface, I suppose one could proceed as follows. Divide the sphere into latitudes and longitudes; let the equator be 0° latitude, choose an arbitrary merdian and call it 0° longitude. Now, at latitude the circle of latitude has radius . So the surface element between latitudes and and longitudes and has area . Hence the surface area of the sphere is

which should work out to be .

also and albeit very uniterestingly by multiplying pir^2 by a factor of D you are changing the amplitude of a waveform graph unless you can specify the exact uses of this and know what you are doing you are easily incorrect

Please stop posting drivel.

umm well..
x= a line
xx=a square
xx+x-xx=a square wave
x(xx)=a cube
but drivel...not likely

Yup, nonsensical drivel.

Laser Tools, Lasers, Applications, Laser System Products, Solutions hmm this nonsence is faster than you

Originally Posted by fiveworlds

umm well..
x= a line
xx=a square
xx+x-xx=a square wave
x(xx)=a cube
but drivel...not likely

Originally Posted by fiveworlds

Laser Tools, Lasers, Applications, Laser System Products, Solutions hmm this nonsence is faster than you

What on earth goes on inside your skull? Every time you post it's like walking into Dali painting or a Becket play.

x= a line
xx=a square
xx+x-xx=a square wave
x(xx)=a cube

Would you care to explain this, apparently meaningless notation?

And what the heck does it have to do with a purveyor of laser systems?

Originally Posted by fiveworlds

also and albeit very uniterestingly by multiplying pir^2 by a factor of D you are changing the amplitude of a waveform graph unless you can specify the exact uses of this and know what you are doing you are easily incorrect

Wrong. Everyone knows that you have to multiply by E, not D. Then -- and only then -- the waveform graph will be sinusoidally rectified. Contumely.

dywyddr is always on about me making coherent replies links to coherent

Originally Posted by fiveworlds

dywyddr is always on about me making coherent replies links to coherent

Doh. Even your jokes are incomprehensible.

You need to take a course in communication skills or something. Posting in shorthand isn't really doing you any favours.

ABLSGR8TaNo

Originally Posted by fiveworlds

ABLSGR8TaNo

Regrettably, that's about the most coherent thing you've posted.

75,13,3,39,16,8? protons

2, 4, 6, 8?
Garden gate.

fun. Tk might i ask you refer to E and not D since both could be a number surely it would be irrelevant what you called it. x^2 for example is the same as x*x or a*a or b*b provided a=b=x of course. Secondly i dont see why it is even necessary for a waveform to be sinusoidally rectified in order to be a waveform but surely Asin(@) applies where A is the amplitude of the wave. This would still hold for x*x etc where x is a certain distance between two points ie length and breadth for a square or length*amplitude. You are doing the exact same with the asin(@) transformations. The main difference being that sinx is bounded on the x axis between 0 and 2pi.

Some threads regrettably regress rather than progress, which results in consummate waste of electronic storage capacity. jocular

Originally Posted by fiveworlds

fun. Tk might i ask you refer to E and not D since both could be a number surely it would be irrelevant what you called it. x^2 for example is the same as x*x or a*a or b*b provided a=b=x of course. Secondly i dont see why it is even necessary for a waveform to be sinusoidally rectified in order to be a waveform but surely Asin(@) applies where A is the amplitude of the wave. This would still hold for x*x etc where x is a certain distance between two points ie length and breadth for a square or length*amplitude. You are doing the exact same with the asin(@) transformations. The main difference being that sinx is bounded on the x axis between 0 and 2pi.

What you are failing to take into account is the distributivity of hyperbolic functions with complex arguments that are Abelian, but not perfunctory. If you parse the bases without orthogonality, you are led ineluctably to a Class 3 Hausdorff homeomorphism.

Now is that clearer?

a little something i didnt know could you redirect me to the solution to this problem

You might find what you want here: New on the snarXiv

so basically instead of awnsering my question redirect to paper generator snarXiv - Wikipedia, the free encyclopedia basically this website i may have to get rid of a few more incorrect mathsbooks

It makes as much sense as 90% of what you write.

its a pity that its typed so

Originally Posted by fiveworlds

its a pity that its typed so

The quality of the typing appears to be symptomatic of the "thought processes" behind it.

then perhaps the 'thought processes' could learn something for a change. Can you explain to me the chemical reactions grass undergoes as it passes through a cows digestive system?