```Date: Mar 8, 2009 10:36 PM
Author: Kirby Urner
Subject: Pentacap

Per the post below, here's a case where the entry in Wikipedia has an incorrect formula, an opportunity for someone to put it right.  I haven't done so at this point,but maybe as a school project...?Note the provided formula for Height (H), can't be rightbecause linear dimensions scale proportionately, linearly, i.e. if you double edges 'a', you thereby double height 'h'.  What's provided is a non-linear function though.http://www.flickr.com/photos/17157315@N00/3339452003/(what it was before fixing)http://en.wikipedia.org/wiki/Pentagonal_pyramid(entry in question)Kirby--- In synergeo@yahoogroups.com, "coyote_starship" <kirby.urner@...> wrote:--- In synergeo@yahoogroups.com, "coyote_starship" <kirby.urner@> wrote:>> --- In synergeo@yahoogroups.com, Adrian Rossiter <adrian_r@> wrote:> > ...> > > For the unit edge icosahedron the pyramid height is therefore> > > >     1/sqrt(phi+2) = approx .5257> >> > DAve also got back to me with this same answer, expressed as> (1/sin(72))/2.> Going by this site, and setting a = e, solving for h:http://mathworld.wolfram.com/PentagonalPyramid.htmlh = a * sqrt((5 - sqrt(5))/10)>>> a = 1>>> h = a * sqrt((5 - sqrt(5))/10)>>> h0.52573111211913359Whoever did the Wikipedia entry did the algebra wrong somehow:http://en.wikipedia.org/wiki/Pentagonal_pyramidKirby> In Python:> > >>> from math import sin, radians> > >>> (1/sin(radians(72)))/2> 0.52573111211913359> > >>> phi = (1 + sqrt(5))/2> > >>> 1/sqrt(phi + 2)> 0.52573111211913359> > He also sent me a vZome and a link to an old diagram:> > http://www.flickr.com/photos/17157315@N00/3340111392/> > http://www.flickr.com/photos/17157315@N00/3339287089/> > Wikipedia is clearly borked.  I might post something to the > Math Forum, see if that clues anyone.> > Kirby>--- End forwarded message ---
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