Spherical Angle Math: Pyramid Angles Constant?

In summary, there are mathematical terms that describe 3D angles, such as solid angles and the sum of outer angles in a pyramid is constant. However, the sum of inner angles is not constant. For more information, refer to the article provided.
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ddddd28
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Hi,
Calculating the angles in 3D shapes can be a very frustrating and annoying thing. So, I was wondering, are there any mathematical terms, which describe a 3d angles?( "angles" between three lines- part of a sphere)
If there are such terms, suppose a triangular pyramid. Is the sum of those "angles" is a constant? just as the sum of angles in a triangle is 180 degrees.
 
Mathematics news on Phys.org

1. What is a Spherical Angle?

A spherical angle is a measurement of the amount of rotation between two intersecting lines on a sphere. It is typically measured in degrees or radians.

2. How is a Spherical Angle calculated?

To calculate a spherical angle, you need to know the radius of the sphere and the lengths of the two intersecting lines. Then, you can use the formula: θ = r * (α + β - γ), where θ is the spherical angle, r is the radius of the sphere, and α, β, and γ are the angles formed by the intersection of the lines on the surface of the sphere.

3. What is the Pyramid Angles Constant?

The Pyramid Angles Constant is a mathematical constant that represents the spherical angle formed at the apex of a regular pyramid. It is equal to 2π minus the dihedral angle of the pyramid.

4. How is the Pyramid Angles Constant used in Spherical Angle Math?

The Pyramid Angles Constant is used in Spherical Angle Math to calculate the spherical angles of a pyramid. It is incorporated into the formula for calculating spherical angles, and can be used to find the spherical angles of any regular pyramid with a given radius and intersecting lines.

5. Why is understanding Spherical Angle Math important for scientists?

Spherical Angle Math is important for scientists because it allows for precise measurements and calculations involving objects on a spherical surface, such as the Earth or other planets. It is also used in fields such as astronomy and geography, where accurate measurements of spherical angles are necessary for understanding and predicting celestial and geographical phenomena.

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