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Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ ′ = 180° − γ. The figure on right shows the point C, the side b and the angle γ as the first solution, and the point C ′, side b ′ and the angle γ ′ as the ...
A singular solution in this stronger sense is often given as tangent to every solution from a family of solutions. By tangent we mean that there is a point x where y s (x) = y c (x) and y' s (x) = y' c (x) where y c is a solution in a family of solutions parameterized by c. This means that the singular solution is the envelope of the family of ...
The self-similar solution of the second kind also appears in different contexts such as in boundary-layer problems subjected to small perturbations, [8] as was identified by Keith Stewartson, [9] Paul A. Libby and Herbert Fox. [10] Moffatt eddies are also a self-similar solution of the second kind.
The one anisotropic shape whose excluded volume can be expressed analytically is the spherocylinder; the solution of this problem is a classic work by Onsager. [6] The problem was tackled by considering the distance between two line segments, which are the center lines of the capped cylinders. Results for other shapes are not readily available.
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ExploreLearning is a Charlottesville, Virginia-based education technology company that operates a large library of interactive online simulations for mathematics and science education in grades 3–12 called 'Gizmos'. ExploreLearning also makes Reflex, an online, game-based system for math fact memorization. [1]
Animation of the additive synthesis of a triangle wave with an increasing number of harmonics. See Fourier Analysis for a mathematical description.. It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by π) and multiplying the amplitude of the ...