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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 ...
G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular) G2 (Aberdeen J projectile) G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive) G6 (flatbase, 6 calibers long secant ogive) G7 (long 7.5° boat-tail, 10 calibers tangent ogive, preferred by some manufacturers for very-low-drag bullets [12])
G1 or Ingalls (flatbase with 2 caliber (blunt) nose ogive - by far the most popular) [59] G2 (Aberdeen J projectile) G5 (short 7.5° boat-tail, 6.19 calibers long tangent ogive) G6 (flatbase, 6 calibers long secant ogive) G7 (long 7.5° boat-tail, 10 calibers secant ogive, preferred by some manufacturers for very-low-drag bullets [60])
The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. [2] Leonhard Euler used it to evaluate the integral ∫ d x / ( a + b cos x ) {\textstyle \int dx/(a+b\cos x)} in his 1768 integral calculus textbook , [ 3 ] and Adrien-Marie Legendre described ...
The osculating circle provides a way to understand the local behavior of a curve and is commonly used in differential geometry and calculus. More formally, in differential geometry of curves , the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p ...
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 ...
is singular at the origin, because both partial derivatives of f(x, y) = y 2 − x 3 − x 2 vanish at (0, 0). Thus the Zariski tangent space to C at the origin is the whole plane, and has higher dimension than the curve itself (two versus one). On the other hand, the tangent cone is the union of the tangent lines to the two branches of C at ...
The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is 1 / 2 (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan 1 / 2 (a + b) = (sin a + sin b) / (cos a + cos b).