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 right
because 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.html

h = a * sqrt((5 - sqrt(5))/10)

>>> a = 1
>>> h = a * sqrt((5 - sqrt(5))/10)
>>> h

0.52573111211913359

Whoever did the Wikipedia entry did the algebra wrong somehow:

http://en.wikipedia.org/wiki/Pentagonal_pyramid

Kirby


> 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 ---