Also adhering to from Gauss, a sphere can not be mapped to your aircraft when retaining equally parts and angles. As a result, any map projection introduces some kind of distortion.
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The circumference of a sphere is outlined because the length of The good circle of the sphere. It is the total boundary of the great circle. The great circle could be the one particular which contains the middle along with the diameter with the sphere.
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The aircraft is the only real other area with A 3-parameter family of transformations (translations along the x- and y-axes and rotations round the origin). Round cylinders are the sole surfaces with two-parameter people of rigid motions along with the surfaces of revolution and helicoids are the one surfaces which has a just one-parameter spouse and children.
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The girth of the surface will be the circumference on the boundary of its orthogonal projection on to the plane. Every of these Qualities implies another.
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This equation displays the placement vector and tangent aircraft at a point are often orthogonal to each other. Furthermore, the outward-dealing with regular vector is equal to the position vector scaled by one/r.
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