The projection in which meridians and parallels are projected onto a plane tangent to the sphere from a point on the earth's surface opposite to the point of tangency is the

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Multiple Choice

The projection in which meridians and parallels are projected onto a plane tangent to the sphere from a point on the earth's surface opposite to the point of tangency is the

Stereographic projection maps points from the sphere onto a plane tangent to the sphere by drawing lines from the point on the sphere opposite the tangency through the sphere to intersect that tangent plane. This construction is exactly what the description specifies: a plane tangent at the point of tangency and projection from the diametrically opposite point. Because of this setup, angles are preserved locally (the projection is conformal), and circles on the sphere map to circles or lines on the plane. Other projections use different geometries—Mercator uses a cylinder and projection from the sphere’s center, orthographic projects orthogonally from infinity onto a plane, and cylindrical equal-area maps from a cylinder without this opposite-point tangential projection—so they don’t match the described method.

Stereographic projection maps points from the sphere onto a plane tangent to the sphere by drawing lines from the point on the sphere opposite the tangency through the sphere to intersect that tangent plane. This construction is exactly what the description specifies: a plane tangent at the point of tangency and projection from the diametrically opposite point. Because of this setup, angles are preserved locally (the projection is conformal), and circles on the sphere map to circles or lines on the plane. Other projections use different geometries—Mercator uses a cylinder and projection from the sphere’s center, orthographic projects orthogonally from infinity onto a plane, and cylindrical equal-area maps from a cylinder without this opposite-point tangential projection—so they don’t match the described method.

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