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Retweet of SwiftOnSecurity

2015 Jun 28, 7:01
If The Matrix was an option, I'd re-up every year.
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Deriving a Non-Recursive Fibonacci Function Using Linear Algebra

2008 Aug 20, 10:51

In my Intro to Algorithms course in college the Fibonacci sequence was used as the example algorithm to which various types of algorithm creation methods were applied. As the course went on we made better and better performing algorithms to find the nth Fibonacci number. In another course we were told about a matrix that when multiplied successively produced Fibonacci numbers. In my linear algebra courses I realized I could diagonalize the matrix to find a non-recursive Fibonacci function. To my surprise this worked and I found a function.
The Nth Fibonacci value is (1 + sqrt(5))^N - (1 - sqrt(5))^N all over sqrt(5) * 2^N
Looking online I found that of course this same function was already well known. Mostly I was irritated that after all the algorithms we created for faster and faster Fibonacci functions we were never told about a constant time function like this.

I recently found my paper depicting this and thought it would be a good thing to use to try out MathML, a markup language for displaying math. I went to the MathML implementations page and installed a plugin for IE to display MathML and then began writing up my paper in MathML. I wrote the MathML by hand and must say that's not how its intended to be created. The language is very verbose and it took me a long time to get the page of equations transcribed.

MathML has presentation elements and content elements that can be used separately or together. I stuck to content elements and while it looked great in IE with my extension when I tried it in FireFox which has builtin MathML support it didn't render. As it turns out FireFox doesn't support MathML content elements. I had already finished creating this page by hand and wasn't about to switch to content elements. Also, in order to get IE to render a MathML document, the document needs directives at the top for specific IE extensions which is a pain. Thankfully, the W3C has a MathML cross platform stylesheet. You just include this XSL at the top of your XHTML page and it turns content elements into appropriate presentation elements, and inserts all the known IE extension goo required for you. So now my page can look lovely and all the ickiness to get it to render is contained in the W3C's XSL.

PermalinkCommentstechnical mathml fibonacci math

MathML to VML/SVG via XSLT (Chris Pollett > Students > Namon)

2008 Mar 8, 11:23"Translating a fragment of MathMLPurpose: To get the MathML matrix related, apply, minus, times, divide, and eq tags to translate to VML and to SVG via XSLT."PermalinkCommentsNamon-Nuttayasakul mathml vml svg xslt xml convert

YouTube - Ghost in the shell- Matrix Parody

2006 Oct 26, 11:23Ghost in the Shell / Matrix TrailerPermalinkCommentsfor:jozhik movie trailer video ghost-in-the-shell gits matrix humor

The Infinite Matrix

2006 Jan 2, 3:51Sci-Fi stories, reviews, and essays.PermalinkCommentsscifi free literature english
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