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Fibonacci numbers/ the golden ratio has always intrigued me. I became especially fascinated when I was a teenager and fantasized of gambling for a living.
Me, too. All of the "strange loops" that tie the Fibonacci numbers to so many other things are just amazing!

For example, if you take your credit card and measure the width and height and divide them, you get the Golden Ratio.

Here's one of my assignments for my freshmen classes:
1. Create an array that contains the first 90 Fibonacci numbers, where fibonacci(1)=1, fibonacci(2)=1, and for n>=3 fibonacci(n)=fibonacci(n-1)+fibonacci(n-2).
2. Use this array that shows that fibonacci(n+1)/fibonacci(n) approaches the value of the Golden Ratio, (1+the square root of 5)/2.
3. Use a two-dimensional array to prove that the following is a magic square.

2 7 6
9 5 1
4 3 8

4. Show that if you replace each number in a magic square by the corresponding Fibonacci number, the sum of products of the rows equals the sum of products of the columns.


:floor:You must have seen 21 this weekend.
Smart, gull! 21 is a Fibonacci number!
 
All of the "strange loops" that tie the Fibonacci numbers to so many other things are just amazing!

For example, if you take your credit card and measure the width and height and divide them, you get the Golden Ratio.

Ah so, that is where Gold card comes from. :biggrin:
 
Me, too. All of the "strange loops" that tie the Fibonacci numbers to so many other things are just amazing!

For example, if you take your credit card and measure the width and height and divide them, you get the Golden Ratio.

Here's one of my assignments for my freshmen classes:
1. Create an array that contains the first 90 Fibonacci numbers, where fibonacci(1)=1, fibonacci(2)=1, and for n>=3 fibonacci(n)=fibonacci(n-1)+fibonacci(n-2).
2. Use this array that shows that fibonacci(n+1)/fibonacci(n) approaches the value of the Golden Ratio, (1+the square root of 5)/2.
3. Use a two-dimensional array to prove that the following is a magic square.

2 7 6
9 5 1
4 3 8

4. Show that if you replace each number in a magic square by the corresponding Fibonacci number, the sum of products of the rows equals the sum of products of the columns.



Smart, gull! 21 is a Fibonacci number!
Is it also a movie or something Mango was referencing? Ah just imdb'd it :wave:
 
For example, if you take your credit card and measure the width and height and divide them, you get the Golden Ratio.

Plastic surgeons use the golden ratio to design their surgeries. Everything from noses to how much to lift a brow to the placement of an areola is determined by the golden ratio. If the distance from brow to chin/distance from hairline to brow = golden ratio then the face shape is ideal, not whether it's oval or square or round or heart.

I'm going to confess to my own OCD induced website passion --

http://www.finestationery.com/

You can design your own invitations, play with fonts, colors, spacing, etc. I spent weeks playing with the Christmas cards. Sometimes I just play on it for fun, designing invitations for parties I don't intend to have....
 
Hey JohnR- I can't find the great website you sent me- the grumpy mom.:lol: Re-hook me up, please!
 
Plastic surgeons use the golden ratio to design their surgeries. Everything from noses to how much to lift a brow to the placement of an areola is determined by the golden ratio. If the distance from brow to chin/distance from hairline to brow = golden ratio then the face shape is ideal, not whether it's oval or square or round or heart.

I'm going to confess to my own OCD induced website passion --

http://www.finestationery.com/

You can design your own invitations, play with fonts, colors, spacing, etc. I spent weeks playing with the Christmas cards. Sometimes I just play on it for fun, designing invitations for parties I don't intend to have....
Here's a great website on that subject.
http://goldennumber.net/face.htm

I'll have to check out your link. Thanks for the info.
 
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