tag:blogger.com,1999:blog-5212354357884270733.post1339245012151394435..comments2017-07-25T16:10:37.890+01:00Comments on Shiny Pebbles and other stuff: What is this thing called i?Rob Lownoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5212354357884270733.post-32073636767644773862017-06-18T08:59:29.022+01:002017-06-18T08:59:29.022+01:00Thanks: I enjoyed putting it together.
Yes, geome...Thanks: I enjoyed putting it together.<br /><br />Yes, geometric algebra is an interesting topic, and gives some powerful tools. It's one of the many things I wish I knew more about, so thanks also for pointing me to your demonstration of how powerful it can be. As it happens I'm in the early stages of writing something where a reference to geometric algebra would be very natural, so I intend to give a link to your article (now that I know about it :-)).Rob Lowhttps://www.blogger.com/profile/01202748963636548483noreply@blogger.comtag:blogger.com,1999:blog-5212354357884270733.post-89996461291160515652017-06-18T03:50:22.229+01:002017-06-18T03:50:22.229+01:00Love this collection of different perspectives.
R...Love this collection of different perspectives.<br /><br />Re: "So we can multiply two dimensional vectors together...what about three dimensional vectors? It turns out that there is no way to do this that is well behaved."<br /><br />There is a way to multiply vectors in any number of dimensions that is well behaved in that it is associative, invertible, and geometrically meaningful: the geometric product. The one catch is that you don't get closure over vectors--it closes over a larger space with other interesting objects in it.<br /><br />I wrote something about why it's nice to be able to multiply and divide by vectors that you might enjoy: http://www.shapeoperator.com/2016/12/12/sunset-geometry/<br /><br />There are some references at the end that point to more thorough treatments.Jasonhttps://www.blogger.com/profile/02263872940831211013noreply@blogger.comtag:blogger.com,1999:blog-5212354357884270733.post-50564922283561975602017-06-15T21:10:16.015+01:002017-06-15T21:10:16.015+01:00Thanks for sharing !Thanks for sharing !Jorge Ramoshttps://www.blogger.com/profile/07567084673889550442noreply@blogger.com