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Tangent ogive nose cone render and profile with parameters and ogive circle shown. Next to a simple cone, the tangent ogive shape is the most familiar in hobby rocketry . The profile of this shape is formed by a segment of a circle such that the rocket body is tangent to the curve of the nose cone at its base, and the base is on the radius of ...
Another attempt at building a ballistic calculator is the model presented in 1980 by Dr. Arthur J. Pejsa. [18] Dr. Pejsa claims on his website that his method was consistently capable of predicting (supersonic) rifle bullet trajectories within 2.5 mm (0.1 in) and bullet velocities within 0.3 m/s (1 ft/s) out to 914 m (1,000 yd) in theory. [19]
An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles ...
The definition of the tangent cone can be extended to abstract algebraic varieties, and even to general Noetherian schemes. Let X be an algebraic variety, x a point of X, and (O X,x, m) be the local ring of X at x. Then the tangent cone to X at x is the spectrum of the associated graded ring of O X,x with respect to the m-adic filtration:
A secant ogive of sharpness = / = The ogive shape of the Space Shuttle external tank Ogive on a 9×19mm Parabellum cartridge. An ogive (/ ˈ oʊ dʒ aɪ v / OH-jyve) is the roundly tapered end of a two- or three-dimensional object. Ogive curves and surfaces are used in engineering, architecture, woodworking, and ballistics.
It is also useful to note an "intrinsic" definition of tangent vectors, which is typical of the generalization of regular surface theory to the setting of smooth manifolds. It defines the tangent space as an abstract two-dimensional real vector space, rather than as a linear subspace of ℝ 3 .
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus , differential geometry , and differential forms .
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve.