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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.
The points P 1, P 2, and P 3 (in blue) are collinear and belong to the graph of x 3 + 3 / 2 x 2 − 5 / 2 x + 5 / 4 . The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too.
First we consider the intersection of two lines L 1 and L 2 in two-dimensional space, with line L 1 being defined by two distinct points (x 1, y 1) and (x 2, y 2), and line L 2 being defined by two distinct points (x 3, y 3) and (x 4, y 4). [2] The intersection P of line L 1 and L 2 can be defined using determinants.
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".
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...