[PDF] first octant of a sphere meaning

What is an example of a spherical octant?

For example, an octant of a sphere is a spherical triangle with three right angles, so that the excess is ? /2. In practical applications it is often small: for example the triangles of geodetic survey typically have a spherical excess much less than 1' of arc. (Rapp Clarke, Legendre's theorem on spherical triangles ).

What is octant in solid geometry?

The horizontal plane shows the four quadrants between x - and y -axis. (Vertex numbers are little-endian balanced ternary.) An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray.

What is the first octant?

Octant (+,+,+) is sometimes referred to as the first octant, although similar ordinal name descriptors are not defined for the other seven octants. The advantages of using the (±,±,±) notation are its unambiguousness, and extensibility for higher dimensions. The following table shows the sign tuples together with likely ways to enumerate them.

How do you find a paraboloid octant in spherical coordinates?

Use cylindrical coordinates. Evaluate (x + y + z) dVE,where E is the solid in the first octant that lies under the paraboloidz = 16 - x2 - y2. Determine an equation for the paraboloid z = x^2 + y^2 in spherical coordinates.