Undergrad Calculating the Surface Area of a Sphere: How Does it Differ?

[AyoubEd]

please , I'm french , so i didn't quite get the meaning of this sentence.

 

[wrobel]

I also have not got it . Area on two dimensional manifold is a 2-form not 1-form

 

[AyoubEd]

it's confusing and wasting my time .
thank you anyway.

 

[nasu]

The formula represents the area of a circular band on the sphere.
Like the shaded area in this image
http://www.mathalino.com/sites/default/files/images/001-total-surface-sphere-integration.jpg
In general is dA=R²sinθdθ but in that text they say that R=1.

 

[jedishrfu]

Yes Nasu has got it right, the differential area of a sphere in spherical coordinates is:

$dA = R^2 sin \theta d\theta d\phi$

and integrating over $d\phi$

and then setting R=1 you get

$Aring = 2\pi * sin \theta d\theta$

 

[AyoubEd]

Thanks a lot guys.
that was very helpful