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Varignon's theorem can also be proved as a theorem of affine geometry organized as linear algebra with the linear combinations restricted to coefficients summing to 1, also called affine or barycentric coordinates. The proof applies even to skew quadrilaterals in spaces of any dimension.
Varignon's theorem is a theorem of French mathematician Pierre Varignon (1654–1722), published in 1687 in his book Projet d'une nouvelle mécanique.The theorem states that the torque of a resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point.
The risk inclination formula uses the principle of moments, or Varignon's theorem, [1] [2] to calculate the first factorial moment of probability in order to define this center point of balance among all confidence weights (i.e., the point of risk equilibration).
In other words, a couple, unlike any more general moments, is a "free vector". (This fact is called Varignon's Second Moment Theorem.) [2] The proof of this claim is as follows: Suppose there are a set of force vectors F 1, F 2, etc. that form a couple, with position vectors (about some origin P), r 1, r 2, etc., respectively.
Vantieghems theorem (number theory) Varignon's theorem (Euclidean geometry) Vieta's formulas ; Vietoris–Begle mapping theorem (algebraic topology) Vinogradov's theorem (number theory) Virial theorem (classical mechanics) Vitali convergence theorem (measure theory) Vitali covering theorem (measure theory) Vitali theorem (measure theory)
Proof without words of Varignon's theorem . Varignon's theorem holds that the midpoints of the sides of an arbitrary quadrilateral are the vertices of a parallelogram, called its Varignon parallelogram. If the quadrilateral is convex or concave (that is, not self-intersecting), then the area of the Varignon parallelogram is half the area of the ...
Transitions Executive Director Mac McArthur agreed. “It’s an ideological thing,” he said. “It’s not a medical thing. It’s not a statutory thing. It’s a philosophical position of the people who started the Recovery Kentucky movement,” who, he said, want to prove “that the 12-step works as well as anything else.”
Varignon parallelogram: Image title: Proof without words of Varignon's theorem by CMG Lee. 1. An arbitrary quadrilateral and its diagonals. 2. Bases of similar triangles are parallel to the blue diagonal. 3. Ditto for the red diagonal. 4.