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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

Dr. Horrible Link Roundup

2008 Aug 10, 3:33

Doctor Horrible's Sing Along Blog is an Internet only show you may have already watched and heard everything about. If you missed this somehow, its a musical by Joss Whedon (Buffy the Vampire Slayer, Firefly) staring Neil Patrick Harris as an aspiring super villian who can't get up the courage to talk to his laundromat crush. Its very funny, fairly geeky, and on the Internet so of course I've enjoyed it thoroughly and have some links to share. It surprised me how many blogs that I don't usually see posting the same things telling me about it: first on Eric's blog, then The Old New Thing, and even Penny-Arcade.

Dr. Horrible's again available online via Hulu with commercial interruption.

Check out the official fan site. They link to such things as the owner of Dr. Horrible's house. He had appeared on Monster House, a reality show about remaking people's homes like Monster Car or Pimp My Ride is about remaking folk's cars, and had his house turned into a evil scientist's lab. Consequently its a perfect fit for Dr. Horrible and in return the owner appears in one of the final scenes and in the credits as the 'Purple Pimp'. Apparently the purple suit is his. Also on his blog you can find out what's happened on that big chair that appears in the show. All I'll say about that is, good thing Neil Patrick Harris wears a lab coat while sitting on it.

At the recent Comic Con some attendees took video of the Dr. Horrible Comic Con panel (video clips contain spoilers) some of which I've grouped together. Besides the videos containing the creators and stars of the musical who are all hilarious (see Felicia Day's comment on twittering) there's also some excellent bits about a possible second installment and information on the impending DVD. To finish off this series of Dr. Horrible links check out this Venn Diagram of Felicia Day's work.

PermalinkCommentsdr. horrible doctor horrible humor link roundup

YouTube: YouTube File Hack (and Others) Download Clips to Your Desktop

2008 Aug 6, 2:56Online and offline YouTube link to video download and conversion tools.PermalinkCommentsyoutube video hack lifehacker flv converter

Lively - Experience another dimension of the web

2008 Jul 9, 11:50Its Lively, Google's in browser Second-Life like thingPermalinkComments3d avatar google im lively online second-life

This may look like a fake Mona Lisa. It isn't. It's a fake of a fake Mona Lisa - Times Online

2008 May 19, 12:28"Were he alive, Konrad Kujau, the man who forged...countless paintings, would no doubt feel a tingle of pride for his great-niece...being prosecuted for forging his signature on hundreds of cheap, Asian-made copies of works such as the Mona Lisa..."PermalinkCommentsart history fraud

FontStruct | Build, Share, Download Fonts

2008 May 9, 9:25Create fonts online, download the resulting font as a TrueType font, embed the font in a webpage. Requires created fonts to be released under creative commons. The embedding method is lame - via Flash.PermalinkCommentsfont development web graphic free cc creativecommons text

Homemade GPS jammers raise concerns

2008 Apr 22, 4:33Reaction to Phrack's howto on GPS jammer. Sounds like the article wants to make it into a bigger issue than it is: "Information in the article that appears in the current issue of the online hacker magazine Phrack potentially puts at risk GPS devices usePermalinkCommentsgps gps-jamming phrack government

frontline: secret history of the credit card: watch online | PBS

2008 Mar 3, 4:18PBS documentary on the history of the credit card. Looks interesting.PermalinkCommentsvia:mattalyst documentary credit-card credit card economics education history tv video

Schmap Licenses my Photos

2008 Feb 18, 1:34

Hotel Diva Computer RoomI got a FlickrMail from Emma J. Williams a bit ago saying that they wanted to use two of my photos in their Schmap San Francisco Guide online travel guide. So now you can see two of my vacation photos on the Westfield San Francisco Shopping Center Schmap page and the Hotel Diva Schmap page.

Westfield San Francisco EscalatorI think its wonderful that digital cameras are at the point where I really don't have to know much about their workings to produce a photo that's reasonable looking. And its thanks to Flickr and searchable tags that Schmap could find my photos. Since my photos on Flickr are all licensed under a Creative Commons license named Attribution-Noncommercial-No Derivative Works 2.0 Generic which only applies to non-commercial uses, Schmap, which is advertisement supported, kindly asked me if they could use my photos. I agreed to their license which was human readable and included wonderful stuff like I get in place attribution and the license is only applicable while Schmap makes their guide freely available online.

Previously I've only heard of folks having their flickr photos used without their permission so I'm glad to know that's not always the case. Or perhaps this is just Schmap's clever method of getting me to blog about them.

PermalinkCommentsme photos creative-commons shcmap flickr

apophenia: a google horror story: what happens when you are disappeared

2008 Feb 11, 4:27Google's adminstrative red tape destroys a person's online identity. There is a happy ending to this story... but it could happen TO YOU!PermalinkCommentsgmail data backup identity google web online article

HEMA - online winkelen

2008 Feb 6, 11:15A flash animated advertisement that starts as a regular website but turns into a kind of Rube Goldberg. I especially appreciate the automated scrolling.PermalinkCommentsadvertising animation art flash browser

LA Weekly - Art+Books - Murakami REVOKed - Shelley Leopold - The Essential Online Resource for Los Angeles

2008 Feb 5, 2:02From BB's article: "In December, graffiti writers AUGER and REVOK modified a billboard advertising the wonderful Takashi Murakami exhibit ... Murakami himself saw online photos of the graffitied billboard and thought it to be "so wonderful, he had to havePermalinkCommentsart graffiti cultural-disobediance murakami via:boingboing

volity.net | Digital Games for Analog People

2008 Jan 29, 11:55Includes an online version of Fluxx. I have my own version of Fluxx over the Internet that I had working but not pretty but this is apparently a publisher sanctioned version so there you go.PermalinkCommentsfluxx game card internet online free

download : vim online

2008 Jan 16, 2:48The place to download GVIM.PermalinkCommentsvim gvim windows install download free opensource pc software tool tools setupnewcomputer

BBC Internet Blog - Brandon's History Of Online BBC

2007 Dec 19, 2:57History of BBC on the Web.PermalinkCommentsvia:sambrook history internet technology bbc web article

The Webby Awards 12 Most Influential Online Videos of All Time

2007 Nov 27, 4:09List of twelve humorous videos that Webby Awards thinks you've already seen.PermalinkCommentshumor internet video videos webby-awards web via:boingboing

Open Library (Open Library)

2007 Jul 26, 12:12The folks at the Internet Archive have created a user modifiable Open Library that intends to catalog all books. As in all of them. Includes links to the books online (Internet Archive for ex.), where to buy (Amazon for ex.), reviews, etc.PermalinkCommentsarchive library opensource wiki research book books literature catalog reference

Technophilia: Where to find public records online - Lifehacker

2007 Jul 23, 3:19List of sites to find public information on folks.PermalinkCommentsbackground search database birthday library identity privacy public phone lifehack

Breaking News: All Online Data Lost After Internet Crash | The Onion - America's Finest News Source

2007 Jul 12, 8:40ONN news story on the crash of the Internet. I blame that Mac the guy was using.PermalinkCommentshumor news onion video internet

Trendsspotting Blog Archive - kids are heavy social network users, they don’t say no to relevant marketing efforts: online surveys and tips for marketersTrendsspotting

2007 Jul 11, 9:54Stats on who uses social networks.PermalinkCommentsresearch reference statistics social web
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