Converting from cartesian to spherical boundaries

Thread starter dan38
Start date Jun 7, 2013
Tags

Cartesian Spherical

In summary, Cartesian boundaries use x, y, and z coordinates to define a point in 3-dimensional space, while spherical boundaries use radius, inclination, and azimuth angles to represent a point on a sphere. Converting from cartesian to spherical boundaries can be useful in certain mathematical or scientific applications, such as in physics or engineering. The formula for converting from cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ) is: r = √(x² + y² + z²), θ = arccos(z / √(x² + y² + z²)), and φ = arctan(y / x). However, spherical coordinates may not be as intuitive or easy to visualize

Jun 7, 2013

dan38

If I had a sphere centred at the origin with x > 0, y > 0 and z > 0
Would the angle boundaries be:
0 < θ < pi/2
0 < α < pi/2
?

Mathematics news on Phys.org

Jun 8, 2013

tiny-tim

Science Advisor

Homework Helper

hi dan38!

dan38 said:

If I had a sphere centred at the origin with x > 0, y > 0 and z > 0
Would the angle boundaries be:
0 < θ < pi/2
0 < α < pi/2
?

yes! …

what is worrying you about that?

What is the difference between cartesian and spherical boundaries?

Cartesian boundaries use x, y, and z coordinates to define a point in 3-dimensional space, while spherical boundaries use radius, inclination, and azimuth angles to represent a point on a sphere.

Why would someone want to convert from cartesian to spherical boundaries?

Converting from cartesian to spherical boundaries can be useful in certain mathematical or scientific applications, such as in physics or engineering, where spherical coordinates may be more appropriate for representing data or solving equations.

What is the formula for converting from cartesian to spherical boundaries?

The formula for converting from cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ) is: r = √(x² + y² + z²), θ = arccos(z / √(x² + y² + z²)), and φ = arctan(y / x).

Are there any limitations to using spherical boundaries?

While spherical boundaries can be useful in certain applications, they may not be as intuitive or easy to visualize as cartesian boundaries. Additionally, spherical coordinates may not be suitable for representing points in non-spherical shapes or objects.

Can spherical boundaries be converted back to cartesian coordinates?

Yes, spherical coordinates can be converted back to cartesian coordinates using the formula: x = r * sin(θ) * cos(φ), y = r * sin(θ) * sin(φ), and z = r * cos(θ).