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The midpoint method computes + so that the red chord is approximately parallel to the tangent line at the midpoint (the green line). In numerical analysis , a branch of applied mathematics , the midpoint method is a one-step method for numerically solving the differential equation ,
Diagonally Implicit Runge–Kutta (DIRK) formulae have been widely used for the numerical solution of stiff initial value problems; [5] the advantage of this approach is that here the solution may be found sequentially as opposed to simultaneously. The simplest method from this class is the order 2 implicit midpoint method.
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.
In geometry, the midpoint polygon of a polygon P is the polygon whose vertices are the midpoints of the edges of P. [1] [2] It is sometimes called the Kasner polygon after Edward Kasner, who termed it the inscribed polygon "for brevity". [3] [4] The medial triangle The Varignon parallelogram
Midpoint theorem may refer to the following mathematical theorems: Midpoint theorem (triangle) Midpoint theorem (conics) Midpoint theorem, describing the properties of medians in a triangle: see Median (triangle) Midpoint theorem, also known as Midpoint formula
Midpoint and infinity are harmonic conjugates. When x is the midpoint of the segment from a to b, then = = By the cross-ratio criterion, the harmonic conjugate of x will be y when t(y) = 1. But there is no finite solution for y on the line through a and b.
In geometry, the midpoint theorem describes a property of parallel chords in a conic. It states that the midpoints of parallel chords in a conic are located on a common line. The common line or line segment for the midpoints is called the diameter. For a circle, ellipse or hyperbola the diameter goes through its center.