parallelogram

Examples of parallelogram in the following topics:

• Forces in Two Dimensions

  • When two forces act on a point particle, the resulting force or the resultant (also called the net force) can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the parallelogram.

• Addition, Subtraction, and Multiplication

  • Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers A and B, interpreted as points of the complex plane, is the point X obtained by building a parallelogram, three of whose vertices are O, A, and B (as shown in ).
  • Addition of two complex numbers can be done geometrically by constructing a parallelogram.

• The Cross Product

  • The magnitude of vector $c$ is equal to the area of the parallelogram made by the two original vectors.

• Technological Advancements under the Song

  • Yang Hui also provided rules for constructing combinatorial arrangements in magic squares, provided theoretical proof for Euclid's forty-third proposition about parallelograms, and was the first to use negative coefficients of "x" in quadratic equations.