Puzzle Description:

Phi (pronounced fee) is the symbol for the Golden Ratio (1.6180339887). Fi is for Fibonacci Spiral. The Golden Ratio is the foundation of beautiful art and architecture, and can be seen in the beauty of nature everywhere. The Ho-Hum is for those who are bored with the mysteries of math. I for one find it rather fascinating.

#1: Teresa K (fasstar) on May 24, 2009 [SPOILER]

This puzzle is just an approximation and is not exact. The Golden Ratio can be seen in the relationship of the lengths of the line segments. Along the bottom row, for instance, the ratio of the shorter segment to the longer segment is the same as the ratio of the longer segment to the sum of both segments.

a + b is to a as a is to b
o-------a-------o----b----o

Phi = (a+b)/a = a/b

It kept looking like a whale. I started with the outer border and worked my way inside. Fun. :-)

I thought it was interesting, and I didn't know the pronunciation of phi, so that comment was interesting.

A very different puzzle. Very interesting and a fun solve.

Thanks, guys. Not my best puzzle, but I do like to make them unique, educational and interesting. Hope this one did the trick.

Ho Hum is my cousins' band in Little Rock.

There's a wonderful Disney cartoon that explains all about the Golden Ratio called "Donald in Mathmagic Land". It's on YouTube. :-)

Thanks for the info, Meg. If it's a Disney film, then it is probably at a level I can understand. :-)
http://www.youtube.com/watch?v=P_ssR7M5Px0

I kept thinking Eeyore from Winnie the Pooh, until I saw the numbers popping up (with the "ho hum"). Quick, easy, fun, and informative. What more could we possibly ask for?!

Thanks, Joe. What more could you ask for? Well, if you like Winnie the Pooh, here is one of his friends (I won't tell you which one):
http://webpbn.com/index.cgi?id=5118

...so I've been pronouncing "phi beta kappa" wrong all these years?...sigh...er, I mean psi.

Oh my gosh, JoDeen, that's a good question. I wonder... everyone I know pronounces it like fi. I investigated a little further and found that both pronunciations are correct. The Greek pronunciation of Phi is fee and the American preferred pronunciation is fi.
http://goldennumber.net/pronounce.htm

I think it's funny that we have an American pronunciation of a Greek word. Why not keep it the original way? Why did anyone even change it anyway?

I seriously see an elephant. I made the 6 into an eye with an eyebrow over it and made the phi into an ear. The curl is the trunk and he's just sort of hunched over. I love the idea, though I'm more used to using it in physics to represent an angle.

i saw an elephant, too. very interesting lesson :-)

Filled in the five solid lines and got about three columns from the left when i realized exactly what this was going to be...of course aesthetic theory is right up my alley.

Nice puzzle! I recognized the Fibonacci spiral very early on, but still solving the rest was a decent challenge, especially with the Phi and the 1.6 in the middle, adding some extra complexity.

Goto next topic

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