- #1
Calculating the Surface Area of a Sphere: How Does it Differ?
- Context: Undergrad
- Thread starter AyoubEd
- Start date
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- Tags
- Area Differential Sphere
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Discussion Overview
The discussion revolves around the calculation of the surface area of a sphere, particularly focusing on the interpretation of the formula and its application in spherical coordinates. Participants express confusion regarding the mathematical representation and the meaning of certain terms.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- Some participants express confusion about the meaning of specific mathematical terms, indicating a lack of clarity in the discussion.
- One participant asserts that the area on a two-dimensional manifold is a 2-form, not a 1-form, suggesting a conceptual distinction in the mathematical framework.
- Another participant clarifies that the formula discussed represents the area of a circular band on the sphere, providing a reference image for context.
- A participant provides the differential area formula in spherical coordinates, stating that integrating over this formula leads to a specific expression for the area of a circular band.
- There is acknowledgment of helpfulness from some participants, indicating that the discussion has provided some clarity despite initial confusion.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the interpretation of the mathematical terms and concepts, with multiple viewpoints expressed regarding the nature of the area calculation.
Contextual Notes
Some limitations include potential misunderstandings of mathematical terminology and the dependence on specific definitions of forms in the context of differential geometry.
- #2
wrobel
Science Advisor
- 1,278
- 1,079
I also have not got it . Area on two dimensional manifold is a 2-form not 1-form
- #3
AyoubEd
- 10
- 2
it's confusing and wasting my time 
.
thank you anyway.
.thank you anyway.
- #4
nasu
Homework Helper
- 4,472
- 921
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.
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.
- #5
jedishrfu
Mentor
- 15,681
- 10,475
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##
##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##
- #6
AyoubEd
- 10
- 2
Thanks a lot guys.
that was very helpful
that was very helpful
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