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The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). [2] It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital , but Leonhard Euler first elaborated the subject, beginning in 1733.
For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain.
The Chiesa del Purgatorio, Ragusa: the facade are angled (canted) back from the centre. County Hall, Aylesbury with canted recesses. A cant in architecture is an angled (oblique-angled) line or surface that cuts off a corner. [1] [2] Something with a cant is canted. Canted façades are a typical of, but not exclusive to, Baroque architecture.
This article summarizes several identities in exterior calculus, a mathematical notation ... ( Hodge dual of constant function 1 is the volume form) Co-differential ...
The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem. cofunction A function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles. [10] This definition typically applies to trigonometric functions.
When the sagitta is small in comparison to the radius, it may be approximated by the formula [2] s ≈ l 2 8 r . {\displaystyle s\approx {\frac {l^{2}}{8r}}.} Alternatively, if the sagitta is small and the sagitta, radius, and chord length are known, they may be used to estimate the arc length by the formula
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem [1] posed by the 15th-century German mathematician Johannes Müller [2] (also known as Regiomontanus). The problem is as follows: The two dots at eye level are possible locations of the viewer's eye. A painting hangs from a wall.
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 ...
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