world page 6 - Dave's Blog

Deriving a Non-Recursive Fibonacci Function Using Linear Algebra

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.

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.

Finally finished Baroque Cycle Novels

I've finally finished the Baroque Cycle, a historical fiction series set in the 17th and 18th centuries by Neal Stephenson whose work I always enjoy. There were often delays where I'd forget about the books until I had to take plane somewhere, or get discouraged reading about the character's thoughts on economics, or have difficulty finding the next volume, or become more engrossed in other books, projects or video games, and leave the Baroque Cycle books untouched for many months at a time. Consequently, my reading of this series has, I'm ashamed to say, spanned years. After finishing some books which I enjoy I end up hungry for just a bit more to read. For this series I don't need a bit more to read, I'm done with that, but I do want a badge or maybe a medal. Or barring that, college credit in European History and Macro Economics. I can recommend this book to anyone who has enjoyed Neal Stephenson's other work and has a few years of free time to kill.

Dinner with Goodwins at Icon Grill

The Goodwin family, except for Michelle who is taking a class trip to Washington DC and New York, was in Seattle this week. Sarah and I met up with them for dinner last night at the Icon Grill. I enjoy the Icon Grill in general and last night was no exception especially having dinner with the Goodwins which was a lot of fun. It was particularly cold and at one point snowed. The Goodwin's are seeing all the classic tourist attractions in Seattle some of which are depicted in the following 1962 Seattle's Worlds Fair postcard. The postcard is featured on Paleo-Future and unsurprisingly the 1962 Worlds Fair favored Seattle's Space Needle and monorail.