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  2. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    The x and y coordinates of the point of intersection of two non-vertical lines can easily be found using the following substitutions and rearrangements. Suppose that two lines have the equations y = ax + c and y = bx + d where a and b are the slopes (gradients) of the lines and where c and d are the y-intercepts of the lines.

  3. Interpolation inequality - Wikipedia

    en.wikipedia.org/wiki/Interpolation_inequality

    A simple example of an interpolation inequality — one in which all the u k are the same u, but the norms ‖·‖ k are different — is Ladyzhenskaya's inequality for functions :, which states that whenever u is a compactly supported function such that both u and its gradient ∇u are square integrable, it follows that the fourth power of u is integrable and [2]

  4. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the lineline intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...

  5. Linear inequality - Wikipedia

    en.wikipedia.org/wiki/Linear_inequality

    A linear programming problem seeks to optimize (find a maximum or minimum value) a function (called the objective function) subject to a number of constraints on the variables which, in general, are linear inequalities. [6] The list of constraints is a system of linear inequalities.

  6. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    Two linear systems using the same set of variables are equivalent if each of the equations in the second system can be derived algebraically from the equations in the first system, and vice versa. Two systems are equivalent if either both are inconsistent or each equation of each of them is a linear combination of the equations of the other one.

  7. Gagliardo–Nirenberg interpolation inequality - Wikipedia

    en.wikipedia.org/wiki/Gagliardo–Nirenberg...

    The proof is completed by combining the two inequalities. In order to prove the base case, several technical lemmas are necessary, while the remaining values of θ {\displaystyle \theta } can be recovered by interpolation and a proof can be found, for instance, in the original work of Nirenberg.

  8. Desmos - Wikipedia

    en.wikipedia.org/wiki/Desmos

    The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]

  9. Smoothstep - Wikipedia

    en.wikipedia.org/wiki/Smoothstep

    A plot of the smoothstep(x) and smootherstep(x) functions, using 0 as the left edge and 1 as the right edgeSmoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning.