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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 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 ,
If = (+) / for all i, the method is the midpoint rule [2] [3] and gives a middle Riemann sum. If f ( x i ∗ ) = sup f ( [ x i − 1 , x i ] ) {\displaystyle f(x_{i}^{*})=\sup f([x_{i-1},x_{i}])} (that is, the supremum of f {\textstyle f} over [ x i − 1 , x i ] {\displaystyle [x_{i-1},x_{i}]} ), the method is the upper rule and gives an upper ...
The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.
The intersection algorithm begins by creating a table of tuples <offset, type>. For each interval there are three entries: the lower endpoint, the midpoint and the upper endpoint, labelled with types −1, 0 and +1 respectively. Thus the interval c ± r results in the entries <c−r,−1>, <c,0> and <c+r,+1>. These entries are then sorted by ...
Similarly, the shortest diameter of an ellipse is called the minor axis, and the segment from its midpoint (the ellipse's center) to either of its endpoints is called a semi-minor axis. The chords of an ellipse which are perpendicular to the major axis and pass through one of its foci are called the latera recta of the ellipse.
A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. The three cleavers concur at (all pass through) the center of the Spieker circle , which is the incircle of the medial triangle .