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Transverse curves on the surface of a sphere Non-transverse curves on the surface of a sphere. Two submanifolds of a given finite-dimensional smooth manifold are said to intersect transversally if at every point of intersection, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point. [1]
Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection). Elevation – along a curve from a point on the horizon to the zenith, directly overhead. Depression – along a curve from a point on the horizon to the nadir, directly below.
A transversal produces 8 angles, as shown in the graph at the above left: 4 with each of the two lines, namely α, β, γ and δ and then α 1, β 1, γ 1 and δ 1; and; 4 of which are interior (between the two lines), namely α, β, γ 1 and δ 1 and 4 of which are exterior, namely α 1, β 1, γ and δ.
The second potential problem is that even if the intersection is zero-dimensional, it may be non-transverse, for example, if V is a plane curve and W is one of its tangent lines. The first problem requires the machinery of intersection theory, discussed above in detail, which replaces V and W by more convenient subvarieties using the moving lemma.
Ceva's theorem, case 1: the three lines are concurrent at a point O inside ABC Ceva's theorem, case 2: the three lines are concurrent at a point O outside ABC. In Euclidean geometry, Ceva's theorem is a theorem about triangles.
Comparison of tangent and secant forms of normal, oblique and transverse Mercator projections with standard parallels in red. The oblique Mercator projection is the oblique aspect of the standard (or Normal) Mercator projection. They share the same underlying mathematical construction and consequently the oblique Mercator inherits many traits ...
The coronal plane is an example of a longitudinal plane.For a human, the mid-coronal plane would transect a standing body into two halves (front and back, or anterior and posterior) in an imaginary line that cuts through both shoulders.
The radial scale is r′(d) and the transverse scale r(d)/(R sin d / R ) where R is the radius of the Earth. Some azimuthal projections are true perspective projections ; that is, they can be constructed mechanically, projecting the surface of the Earth by extending lines from a point of perspective (along an infinite line through the ...