| Deutsch English Français Italiano |
|
<pan$6398d$b1060b6f$7caf2bb5$5e7aea65@linux.rocks> View for Bookmarking (what is this?) Look up another Usenet article |
From: Farley Flud <ff@linux.rocks> Subject: Mystery of High Dimensions [NOT OT] Newsgroups: comp.os.linux.advocacy Mime-Version: 1.0 Message-Id: <pan$6398d$b1060b6f$7caf2bb5$5e7aea65@linux.rocks> Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Lines: 39 Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!usenet.blueworldhosting.com!diablo1.usenet.blueworldhosting.com!feeder.usenetexpress.com!tr2.iad1.usenetexpress.com!news.usenetexpress.com!not-for-mail Date: Wed, 01 Jan 2025 12:29:57 +0000 Nntp-Posting-Date: Wed, 01 Jan 2025 12:29:57 +0000 X-Received-Bytes: 1573 Organization: UsenetExpress - www.usenetexpress.com X-Complaints-To: abuse@usenetexpress.com We all know that the volume of a cube with each side = 1 is equal to 1. That's because volume = 1^3 = 1. In fact, the volume of any higher dimensional hypercube is also 1 because in any dimension n the volume = 1^n = 1. Example, the volume of a hypercube of 100 dimensions is 1^100 = 1. But what is the volume of a 100D hypersphere of radius = 1 that is inscribed within this 100D hypercube? Answer: π^50/30414093201713378043612608166064768844377641568960512000000000000 = 2.3682021018828293*10^-40 = 0.00000000000000000000000000000000000000023682021018828293 Why so fucking small, when the volume of the containing hypercube is 1.0? In fact, as the dimensions increase further, a hypersphere of radius=1 has a volume that approaches zero. How can this be? Consider a hypersphere of radius = 1 mile. As the dimensions increase the volume will approach 0 cubic miles (i.e. nothing, zip, nada). But the containing hypercube will always have a volume of 1 cubic mile. Oblinux: Maxima CAS was used to do the exact calculations. -- Systemd: solving all the problems that you never knew you had.