- #1

Vrbic

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Thank you for your advice and help.

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In summary, the conversation discusses how to calculate the area of a ring on the surface of a unit sphere using spherical coordinates. It is suggested to construct a new coordinate system with the z-axis passing through the center of the sphere and the center of the circle, and to use the formula \phi= \frac{2\pi r}{R} for the circle's radius. For the general case, numerical approximation is recommended due to the potential complexity of the boundary of the area. However, some theoretical base is needed for this approach.

- #1

Vrbic

- 407

- 18

Thank you for your advice and help.

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- #2

HallsofIvy

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[tex]\int_{0}^{2\pi}\int_0^{\frac{2\pi r}{R}} sin(\theta)d\phi d\theta[/tex].

- #3

Vrbic

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Thank you for your post, I understand , but it was just example, the ring on the ball. I would like to have some procedure for general case of area.HallsofIvy said:andthe center of the circle on the surface of the sphere. Given that the sphere has radius R, a "circle" of radius r with center on the z-axis is given by [itex]\phi= \frac{2\pi r}{R}[/itex]. The area of that circle is

[tex]\int_{0}^{2\pi}\int_0^{\frac{2\pi r}{R}} sin(\theta)d\phi d\theta[/tex].

- #4

tommyxu3

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- #5

Vrbic

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I agree with numerical aprox., but I have to know some theoretical base.tommyxu3 said:

The area of a unit sphere can be calculated using the formula A = 4πr^2, where r is the radius of the sphere and π is a mathematical constant equal to approximately 3.14.

The formula for calculating the area of a ring on a sphere is A = 2πrh, where r is the radius of the sphere and h is the height of the ring (also known as the distance between the center of the sphere and the center of the ring).

No, the area of a sphere is measured in square units just like any other surface area measurement. However, the units used may vary depending on the context (e.g. square meters, square feet, etc.).

The area of a spherical cap can be calculated using the formula A = 2πrh, where r is the radius of the sphere and h is the height of the cap (also known as the distance between the center of the sphere and the top of the cap).

Yes, there is a difference in calculating the area of a sphere and a circle. A circle is a two-dimensional shape, so its area can be calculated using the formula A = πr^2, where r is the radius of the circle. A sphere, on the other hand, is a three-dimensional shape, so its area is calculated using the formula A = 4πr^2.

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