Double concerto Piano, and Timpani" is commonly known by the title "Double Concerto," where the word "double" refers to the two string bodies rather than to the piano and timpani who are not soloists in the conventional sense. Concerti with more than two solo parts may be known by the terms "triple concerto" (Italian: "Concerto triplo", German: "Tripelkonzert"), "quadruple concerto," etc., but not usually when the instruments of the same type (e.g., Vivaldi's Concerto for Four Violins in B minor, catalogued as RV 580 and transcribed for four harpsichords by Bach as BWV 1065). One common arrangement for a triple concerto is
Quadruple product Quadruple product In mathematics, the quadruple product is a product of four vectors in three-dimensional Euclidean space. The name "quadruple product" is used for two different products, the scalar-valued scalar quadruple product and the vector-valued vector quadruple product or vector product of four vectors . The scalar quadruple product is defined as the dot product of two cross products: where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity: or using the determinant: The vector quadruple product is defined as the cross product of two cross products: where a, b, c, d