2004/11/04 by N. Shabot-Marcos, Shabot-Marcos, N., A. Sandoval-Villalbazo +1
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #math.MG
paper · pdf · doi:10.48550/arxiv.math/0411106
2 pages, 1 figure
arxiv created 2004/11/04 · arxiv updated 2009/12/01
This note shows that an interesting property arises when considering the relation between the hypersphere volumes at dimensions n+1 and n, if the hyperspheres circumscribe unitary hypercubes in n+1 and n dimensions, respectively . In the limit of large n, the ratio \fracVn+1Vn is constant and equal to the irrational number √((πe)/(2)). Some consequences of this result are explored.