Re: unlearn trig!
Gerald de Jong <[email protected]> Sun, 18 Sep 2005 16:13:41 +0200
| Newsgroups | gmane.comp.graphics.fluidiom |
|---|---|
| Message-ID | <[email protected]> |
--Apple-Mail-4-569249708 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed On 18-Sep-05, at 13:13, Gerald de Jong wrote: > my suspicion is that Wildberger's insights could lead to a > mathematical simplification of a lot of Fuller's work. there's > something in there, because Fuller was big on rational numbers, > although he took dives into sin and cos when he presumed > necessary. let's revisit that stuff! this might be a nice first example: if you take two adjacent faces of an icosahedron with edge length one and join the far points with a new edge you get a tetrahedron with all edges length one except for the new edge which is length PHI (1.618.., the golden mean). as it turns out, the quadrance volume of this tetrahedron is 1/2. remember that the regular tetrahedron had QV=1. in other words.. take a regular tetrahedron and extend one edge to PHI length, and you half the QV. PS. where's Richard Hawkins when you need 'im? what about the great circles? what about the quantum A and B modules? --Apple-Mail-4-569249708 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=ISO-8859-1 <HTML><BODY style=3D"word-wrap: break-word; -khtml-nbsp-mode: space; = -khtml-line-break: after-white-space; "><DIV><DIV>On 18-Sep-05, at = 13:13, Gerald de Jong wrote:</DIV><BLOCKQUOTE type=3D"cite"><DIV = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; ">my suspicion is that Wildberger's insights could = lead to a mathematical simplification of a lot of Fuller's work.<SPAN = class=3D"Apple-converted-space">=A0 </SPAN>there's something in there, = because Fuller was big on rational numbers, although he took dives into = sin and cos when he presumed necessary.<SPAN = class=3D"Apple-converted-space">=A0 </SPAN>let's revisit that = stuff!</DIV></BLOCKQUOTE></DIV><FONT class=3D"Apple-style-span" = color=3D"#0000DD"><BR class=3D"khtml-block-placeholder"></FONT><DIV><FONT = class=3D"Apple-style-span" color=3D"#0000DD">this might be a nice first = example:=A0 if you take two adjacent faces of an icosahedron with edge = length one and join the far points with a new edge you get a tetrahedron = with all edges length one except for the new edge which is length PHI = (1.618.., the golden mean).=A0 as it turns out, the quadrance volume of = this tetrahedron is 1/2.=A0 remember that the regular tetrahedron had = QV=3D1.</FONT></DIV><DIV><FONT class=3D"Apple-style-span" = color=3D"#0000DD"><BR = class=3D"khtml-block-placeholder"></FONT></DIV><DIV><FONT = class=3D"Apple-style-span" color=3D"#0000DD">in other words.. take a = regular tetrahedron and extend one edge to PHI length, and you half the = QV.</FONT></DIV><DIV><FONT class=3D"Apple-style-span" = color=3D"#0000DD"><BR = class=3D"khtml-block-placeholder"></FONT></DIV><DIV><FONT = class=3D"Apple-style-span" color=3D"#0000DD">PS.=A0 where's Richard = Hawkins when you need 'im?=A0 what about the great circles?=A0 what = about the quantum A and B modules?</FONT></DIV></BODY></HTML>= --Apple-Mail-4-569249708-- ------------------------------------------------------- SF.Net email is sponsored by: Tame your development challenges with Apache's Geronimo App Server. Download it for free - -and be entered to win a 42" plasma tv or your very own Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php