Multidimensional integer trigonometry
In this paper, the authors generalize integer trigonometric functions from two dimensions into arbitrary dimensions. They give a definition of the integer sine of a simplicial cone relating it to integer volume and give a definition of integer arctangent and relate it to Hermite's normal form. This leads naturally to describing the relationship between the values of adjacent cones, transpose cones, and cones which generate the same simplex. This leads to a notion of best approximations of simplicial cones. They also discuss the relationship between integer trigonometry, the Euclidean Algorithm, and continued fractions.
scientific article; zbMATH DE number 7902969
scientific article