The future belongs to those who believe in the beauty of their dreams. — Eleanor Roosevelt
Monthly Archives: February 2012
Meet π’s cousin, φ
So what’s that symbol, you ask? It’s the Greek letter Phi (pronounced FEE).
We’ve all heard of the (in)famous π, or 3.14159265358… Our math teachers pounded this into our heads every year, and the nerds would always hold competitions to see who could recite the most digits of pi. So far, computers have sputtered out over 5 trillion digits of pi.
But another number, just as beautiful as pi, is relatively unknown to the masses. That number is phi, or 1.61803399… It is the number that satisfies the following algebraic equation: (a+b)/a = a/b.
There are many ways of expressing this golden number:
As an infinite series,
As a continued fraction,
As a continued square root, which bears striking resemblance to the above:
But wait, there’s even more:
φ^2 = φ + 1,
and even more surprisingly,
1/φ = φ – 1. Wow!
If that surprised you, this will truly give you a shock:
φ to the nth power is equal to the sum of the previous two integer powers of φ. Check this out:
- φ^3 = φ^2 + φ^1
- φ^4 = φ^3 + φ^2
- φ^n = φ^(n-1) + φ^(n-2)
The same thing goes with negative powers! Try it out!
Thought it couldn’t get even more fascinating? WRONG!
Compare the digits after the decimal point in this table:
| n | phin | phi-n |
|---|---|---|
| 1 | 1.61803398875 | 0.61803398875 |
| 3 | 4.23606797750 | 0.23606797750 |
| 5 | 11.09016994375 | 0.09016994375 |
| 7 | 29.03444185375 | 0.03444185375 |
| 9 | 76.01315561752 | 0.01315561752 |
Lo and behold, the decimal parts in the latter 2 columns are exactly the same! Also notable: this relationship does not exist if n is an even number.
For those of you who are still reading, there is a special link between phi and the Fibonacci series:
Let F(n) = 1, 1, 2, 3, 5, 8, 13, …
WHOA! Who knew?
Home away from home
Hey guys,
I’m currently NOT at home in Seattle right now. In fact, I’m going to be in Yakima over the weekend.
The Internet connection at the Howard Johnson is absolutely abominable, so there won’t be many new media-rich and exciting blog posts. Sorry about that, blame HoJo for putting happy balls on their WiFi antennas.
Till I get back!
–Deathgleaner
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Lack of updates
Apologies to all blog readers, the author has been very busy lately.
He will get back to blogging as soon as he unclogs his brain tubes.
How to present your PowerPoint … in style
By the time you graduate from college, you will probably have made over 100 Power Point presentations, mostly on Microsoft PowerPoint software. Unfortunately, many of us students go through our academic and work lives having to start a presentation in 3 steps:
- Opening the folder that the file is in
- Opening the file
- Clicking “Start Presentation”
Did you know there’s a way to avoid Step 3? At the end of the filename, simply change the extension to .pps. When you click on the filename.pps, it will start your presentation without viewing the ugly PowerPoint editing GUI. Amazing!
NOTE: Changing the extension to .pps will not allow you to edit the presentation. If you wish to edit the presentation, just change the extension back to .ppt or .pptx!
What font is that?
How many times have we seen a font used in a magazine, on a box, or in an advertisement, and wanted to find out what font it is? Up until I discovered WhatTheFont!, I had to go through every font in Word and compare it with the original.
WhatTheFont! is a tool to help you discover, well, what font is being used. You upload an image, and the website splices up the image into many little images containing one letter or symbol. It’s remarkable what it can do for you.
For example, I took this Honey Bunches of Oats cereal box, and put it into the font finder, and voilà: Mushmellow. Now all I had to do was find the font, download, and install it. Within minutes, I was using it to create a parody of the world-famous cereal box.
I hope you will find this tool useful!
Write a letter to yourself … one year from now
Remember when you were young and the teacher would say, on the first day of school, “All right kids, write a letter to yourself one year from now, and at the end of the year, I’ll give the letters back to you?” Now, there’s a website for that (and maybe an app too, who knows?) FutureMe.org is a handy service brought to you by Matt Sly and Jay Patrikios. The concept is simple; you type in your email and message, and click on the Send to the Future! button. In addition, you can make your message public, and add a picture to it. The only disadvantage of the system is that the date has to be at least one month into the future.
Try it out today: http://www.futureme.org/letters.
Want to visualize your music? Try Synthesia!
A long time ago, I covered MuseScore, an application that can typeset your music as well as play it back.
And now, for something completely similar…
Originally developed as a game to train people how to play piano, Synthesia is equally adept at playing back your music. Instead of a bunch of notes on five-line staves, Synthesia uses a Guitar-Hero-esque approach, by translating notes in a MIDI file into colorful falling bars that strike a keyboard. The advantage of this visualization is that everyone, including non-musicians, can understand what’s going on in the music.
Take a look at the videos below:
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