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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

New office, new cubes

2008 Aug 5, 6:32

Second Window OfficeNew Patent CubesMy previous window office was ripped from me when our team moved buildings but now I've got another. The photo is poor because I didn't get the lighting correct and it depicts the office before I've moved all my crap into it. I have a lovely view of our parking lot and freeway which Jane spun as an 'urban view'. At any rate I'm not complaining: I like knowing what its like outside and that there is an outside. The day after I found out about my office, I also got two new patent cubes. I didn't have any pictures last time so I took some now and blacked out their text for fear of laywers.

PermalinkCommentsmicrosoft patent cube office nontechnical

Dark Knight and Mariners Baseball

2008 Aug 4, 8:39

The weekend before last I saw Dark Knight with some friends from work and then we all ate at Z'Tejas after. Like everyone has said and as the name implies Dark Knight is... dark. Dark Knight was a little over the top at times as compared to Batman Begins but I really enjoyed it. Two times during the movie I thought it had ended but I was wrong. The Joker is both frightening (Cringe inducing line "Wanna know how I got these scars?") and humorous ("Where is Harvey Dent? ... You know where Harvey is? You know who he is?", as well as the pencil magic trick). I can certainly recommend it to anyone who enjoyed Batman Begins. The previews included Burn After Reading a new Coen Brother's comedy that I look forward to, and Quantum of Solace which hopefully does the same thing Dark Knight has, keep up the new direction on the refreshed franchise.

Safeco Field Suite photoThis past weekend Sarah and I went to a Mariners baseball game. I think this is the first MLB baseball game I've seen in person. Sarah's company gave out tickets for the game and the use of a suite. Its a room half way up the stadium with comfortable chairs, a mini-fridge built-in to the marble counter-topped center table, and a big flat screen television with the game on it. I suppose that's in case you don't want to turn to the right and sit at the window, or walk out onto the balcony which features three rows of comfy chairs overlooking the field. Anyway there was free food and drinks and I met some of the people Sarah works with.

PermalinkCommentsbaseball batman nontechnical

View from the Safeco Field Suite

2008 Aug 3, 12:53

sequelguy posted a photo:

View from the Safeco Field Suite

PermalinkCommentsseattle washington baseball mariners safecofield

In the Safeco Field Suite

2008 Aug 3, 12:52

sequelguy posted a photo:

In the Safeco Field Suite

PermalinkCommentsseattle me washington baseball mariners safecofield

Safeco Field Suite

2008 Aug 3, 12:52

sequelguy posted a photo:

Safeco Field Suite

PermalinkCommentsseattle washington baseball mariners safecofield

New Patent Cubes

2008 Aug 3, 12:52

sequelguy posted a photo:

New Patent Cubes

PermalinkCommentswork microsoft patent patentcubes

Second Window Office

2008 Aug 3, 12:51

sequelguy posted a photo:

Second Window Office

My new window office, before I took out the old furniture and moved in all of my crap. A lovely view of parking lot and freeway.

PermalinkCommentswork office microsoft windowoffice

Earplug Alarm Clock

2008 Jul 9, 1:37

Dirt PileIn my previous home, just after I moved in, my neighbor which was the city of Redmond's various city government buildings, decided to build a parking structure. This was maybe 30 feet from my window, lasted for at least a year and would regularly wake me up at seven or eight in the morning. Determined to not be so punctual for work, I got earplugs which meant in addition to not hearing the construction outside, I couldn't hear my alarm. I had an idea for a combination ear plug, headphone, alarm clock that I never did anything with, except to write down the phrase "earplug / headphone / alarm clock" on a list that I just now found. In retrospect, I think this problem might be too specific to result in my earplug alarm clock selling well.

PermalinkCommentsidea earplug headphone alarm clock random nontechnical

Trip to Victoria, BC

2008 Jun 25, 12:26

Victoria Marriott Inner HarbourThe weekend before last was Sarah's birthday and as part of that, last weekend we took a trip to Victoria, BC. I've got a map of our trip locations and photos. Not all the photos are on the map but they're all in the trip photo set on Flickr. It turns out there's a lot of tourist intended activities right around our hotel which was in the inner harbor and downtown Victoria area. As such we didn't get a rental car and did a lot of walking.

Sarah in HallwayOn the first day we checked out the Royal British Columbia Museum which had some interesting exhibits in it and the Undersea Garden which was interesting in that its like a floating aquarium but was a bit grimy. There was a group of Japanese tourists next to us during the undersea show in which a diver behind the glass in the ocean would pick up and parade various animal life. The group all repeated the word starfish in unison after the show's narrator and one of the tourists was very excited to see the diver bring over the octopus. The diver made the octopus wave to us while it desperately tried to get away.

British Columbia Parliament BuildingsWe flew in and out of the Victoria International Airport which is a smaller sized airport. Although we needed our passports we didn't need to take off our shoes -- what convenience! The US dollar was just a bit worse than the Canadian dollar which was also convenient. The weather was lovely while we were there and I only got slightly sun burned.

PermalinkCommentsvictoria canada vacation nontechnical

CCTV Graffiti

2008 Jun 24, 10:06

sequelguy posted a photo:

CCTV Graffiti

PermalinkCommentscanada graffiti cctv victoria

Olde Time-y Phone Booth

2008 Jun 24, 10:06

sequelguy posted a photo:

Olde Time-y Phone Booth

PermalinkCommentscanada sarah phonebooth victoria

British Columbia Parliament Buildings

2008 Jun 24, 10:05

sequelguy posted a photo:

British Columbia Parliament Buildings

en.wikipedia.org/wiki/British_Columbia_Parliament_Buildings

PermalinkCommentscanada victoria britishcolumbiaparliamentbuildings

Roses Against Sky

2008 Jun 24, 10:04

sequelguy posted a photo:

Roses Against Sky

PermalinkCommentscanada flower rose victoria sarahtookthisphoto

Sarah in Hallway

2008 Jun 24, 10:03

sequelguy posted a photo:

Sarah in Hallway

PermalinkCommentscanada tree sarah victoria hallway

Mosaic Sign

2008 Jun 24, 10:02

sequelguy posted a photo:

Mosaic Sign

PermalinkCommentscanada sign mosaic victoria medgrill

Graffiti

2008 Jun 24, 10:02

sequelguy posted a photo:

Graffiti

I thought the phrase 'Im seein robots' was funny.

PermalinkCommentscanada graffiti victoria robots

Craigdarroch Castle

2008 Jun 24, 10:01

sequelguy posted a photo:

Craigdarroch Castle

PermalinkCommentscanada victoria craigdarrochcastle

Me in front of Craigdarroch Castle

2008 Jun 24, 10:00

sequelguy posted a photo:

Me in front of Craigdarroch Castle

PermalinkCommentscanada me victoria craigdarrochcastle sarahtookthisphoto
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