Re: unlearn trig!
Gerald de Jong <[email protected]> Sun, 18 Sep 2005 09:53:33 +0200
| Newsgroups | gmane.comp.graphics.fluidiom |
|---|---|
| Message-ID | <[email protected]> |
--Apple-Mail-1-546442160 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed your server says: You don't have permission to access /2005/09/build- it-green.html on this server. i'm rewriting some of the Fluidiom client-side code right now, removing the three-worlds metaphor in favor of a simple way to collect cool evolutionary artifacts. there will be folders with passwords, and it will be easy to pick up somebody else's creation and evolve it. the result will end up in your folder. this is in preparation for presenting at the conference: http://como.vub.ac.be/bnaic2005/ Kirby, when i read that chapter of the book, talking about quadrance and spread instead of distance and angle, i was struck by a memory from a few years back. do you remember when i agonized over the problem of determining the volume of a tetrahedron based on its six lengths? it took me two weeks of train rides to figure out how to do it, and then to avoid getting lost in the math i built a program to handle all the terms. it turned out to be already discovered, of course. no surprise that Euler had expressed it at some point, although his equation didn't hilight the geometry. now with quadrances, it makes even more sense. take the 6 quadrances instead and the volume formula turns out to look a lot nicer. every term in the formula was a distance squared which this guy now successfully argues is more primal than the distance itself! it's like this: add the products of the quadrances of the twelve open triangles, subtract the products of the quadrances of the four closed triangles, and then subtract the products times the sums of the quadrances of three pairs of opposite edges. that might sound a little complicated, but it's worlds less complicated than the alternative. now i'm thinking that maybe there's something more primitive than volume, just as the quadrance is more primitive than distance. On 18-Sep-05, at 1:05, Kirby Urner wrote: > Thanks for the heads-up Gerald. I downloaded and studied Chapter > 1. Looks > interesting. I noted your sending a heads up in my blog: > http://worldgame.blogspot.com/2005/09/build-it-green.html > > Kirby > > PS: although we didn't work on the client-side-only version of > Fluidiom, > pre-OSCON, I had a good internet connection and we watched your > creatures > evolve for a little while. http://www.4dsolutions.net/ocn/ > oscon2005.html > > >> somebody's come up with something that makes sin/cos trigonometry >> obsolete, it seems. seriously! >> --Apple-Mail-1-546442160 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; "><P style=3D"margin: 0.0px 0.0px = 21.0px 0.0px"><FONT class=3D"Apple-style-span" face=3D"Times" = size=3D"4"><FONT class=3D"Apple-style-span" size=3D"4"><SPAN = class=3D"Apple-style-span" style=3D"font-size: 16px;">your server = says:=A0=A0</SPAN></FONT><SPAN class=3D"Apple-style-span" = style=3D"font-size: 16px;">You don't have permission to access = /2005/09/build-it-green.html on this server.</SPAN></FONT></P><DIV = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; "><FONT class=3D"Apple-style-span" face=3D"Times" = size=3D"4"><SPAN class=3D"Apple-style-span" style=3D"font-size: = 16px;"></SPAN></FONT></DIV><DIV>i'm rewriting some of the Fluidiom = client-side code right now, removing the three-worlds metaphor in favor = of a simple way to collect cool evolutionary artifacts.=A0 there will be = folders with passwords, and it will be easy to pick up somebody else's = creation and evolve it.=A0 the result will end up in your = folder.</DIV><DIV><BR class=3D"khtml-block-placeholder"></DIV><DIV>this = is in preparation for presenting at the conference:</DIV><DIV><A = href=3D"http://como.vub.ac.be/bnaic2005/">http://como.vub.ac.be/bnaic2005/= </A></DIV><DIV><BR class=3D"khtml-block-placeholder"></DIV><DIV>Kirby, = when i read that chapter of the book, talking about quadrance and spread = instead of distance and angle, i was struck by a memory from a few years = back.=A0 do you remember when i agonized over the problem of determining = the volume of a tetrahedron based on its six lengths?=A0 it took me two = weeks of train rides to figure out how to do it, and then to avoid = getting lost in the math i built a program to handle all the terms.=A0 = it turned out to be already discovered, of course.=A0 no surprise that = Euler had expressed it at some point, although his equation didn't = hilight the geometry.</DIV><DIV><BR = class=3D"khtml-block-placeholder"></DIV><DIV>now with quadrances, it = makes even more sense.=A0 take the 6 quadrances instead and the volume = formula turns out to look a lot nicer.=A0 every term in the formula was = a distance squared which this guy now successfully argues is more primal = than the distance itself!</DIV><DIV><BR = class=3D"khtml-block-placeholder"></DIV><DIV>it's like this:=A0 add the = products of the quadrances of the twelve open triangles, subtract the = products of the quadrances of the four closed triangles, and then = subtract the products times the sums of the quadrances of three pairs of = opposite edges.=A0 that might sound a little complicated, but it's = worlds less complicated than the alternative.</DIV><DIV><BR = class=3D"khtml-block-placeholder"></DIV><DIV>now i'm thinking that maybe = there's something more primitive than volume, just as the quadrance is = more primitive than distance.</DIV><BR><DIV><DIV>On 18-Sep-05, at 1:05, = Kirby Urner wrote:</DIV><BLOCKQUOTE type=3D"cite"><DIV = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; ">Thanks for the heads-up Gerald.<SPAN = class=3D"Apple-converted-space">=A0 </SPAN>I downloaded and studied = Chapter 1.<SPAN class=3D"Apple-converted-space">=A0 = </SPAN>Looks</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; ">interesting.<SPAN = class=3D"Apple-converted-space">=A0 </SPAN>I noted your sending a heads = up in my blog:</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; "><A = href=3D"http://worldgame.blogspot.com/2005/09/build-it-green.html">http://= worldgame.blogspot.com/2005/09/build-it-green.html</A></DIV><DIV = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style=3D"margin-top: = 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; = ">Kirby</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; ">PS:<SPAN class=3D"Apple-converted-space">=A0 = </SPAN>although we didn't work on the client-side-only version of = Fluidiom,</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; ">pre-OSCON, I had a good internet = connection and we watched your creatures</DIV><DIV style=3D"margin-top: = 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">evolve = for a little while.<SPAN class=3D"Apple-converted-space">=A0 </SPAN><A = href=3D"http://www.4dsolutions.net/ocn/oscon2005.html">http://www.4dsoluti= ons.net/ocn/oscon2005.html</A></DIV><DIV style=3D"margin-top: 0px; = margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: = 14px; "><BR></DIV> <BR><BLOCKQUOTE type=3D"cite"><DIV style=3D"margin-top:= 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; = ">somebody's come up with something that makes sin/cos = trigonometry</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 0px; ">obsolete, it seems.<SPAN = class=3D"Apple-converted-space">=A0 </SPAN>seriously!</DIV><DIV><BR = class=3D"khtml-block-placeholder"></DIV></BLOCKQUOTE></BLOCKQUOTE></DIV></= BODY></HTML>= --Apple-Mail-1-546442160-- ------------------------------------------------------- SF.Net email is sponsored by: Tame your development challenges with Apache's Geronimo App Server. 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