What dimensionality is required? The corner is less than or equal to 1 trillionth of it.
The problem's question is "What is the minimum positive integer dimensionality of a n-dimensional parallelogram such that a corner figure of the parallelogram has a volume less than or equal to one-trillionth of the volume of the entire non-degenerate parallelogram?"
A parallelogram is non-degenerate when the edge vectors when assembled into a matrix form a matrix with a non-zero determinant, i.e., the edge vectors are independent.
A corner figure is a simplex formed by selecting a corner vertex of the parallelogram and the edges that meet at that vertex and then forming triangular faces, etc., by joining adjacent vertices at the other ends of those edges. Since the question is only about volume ratios, neither the angles between edge vectors nor the edge vector lengths are specified herein.
The answer is 15.
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1 solution
In general the n-dimensional volume of a corner figure of an n-cube will be 1/n!, where n! stands for "n factorial," obtained by, multiplying together the first n numbers.
15! == 1307674368000 > 10^12.