From kragen@dnaco.net Mon Jun 29 15:32:05 1998 Date: Mon, 29 Jun 1998 15:32:04 -0400 (EDT) From: Kragen To: michael Subject: Re: An Introduction to Geodesic Domes Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Keywords: X-UID: 148 Status: O X-Status: You write: > A sphere represents the least amount of material surface area possible > to enclose a given volume of space. When bisected, the half sphere > becomes one of the most efficient shapes known to enclose a given floor > area. Any "dent" made in the half sphere decreases the area enclosed > while the total surface area stays the same. The first sentence is correct. The second sentence is not, if "floor area" means "ground area". The third sentence is correct if "the area" means "the volume of space", but not if "the area" means "the ground area". To enclose a given amount of ground area with the least possible amount of material, you just lay a roof on top of the ground and need no walls. If you have other constraints (such as needing to use the ground area to live on, sleep, eat, etc.) the solution is different. Usually, for human dwellings, you need to have a certain amount of vertical space enclosed directly above the ground -- say, ten feet or so. The most efficient way to enclose a given amount of ground area with ten feet of free space above it is to build a cylinder ten feet high and with a cross-sectional area equal to the ground area you want to enclose. If you're building multi-story structures, though, you can enclose floor area approximately equal to the volume of your house divided by the height of each floor. The approximation is spoiled a bit by the non-vertical walls of a dome. In particular, you can have a 40-foot-diameter hemispherical dome that has considerably more surface area than a 40-foot-diameter 10-foot-high cylinder, but without enclosing any more usable floor area (if you define "usable" to mean "having ten feet of free space above it".) Peace, Kragen