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 January 18th, 2013, 10:56 AM #1 Newbie   Joined: Jan 2013 Posts: 8 Thanks: 0 pi clock Hello everyone. I have been trying to solve a pi clock which is attach. I figured out most of the positioins except the 5 and 7 positions. 5 = RANK([pi,((S**1)**5)) 7 = |pi, L(7,3)| On the 5 position, I am guessing S is a sum series. I am not sure if the power is a 1. As for the 7 position, I think the L is a Eulidean norm vector.
 January 18th, 2013, 11:04 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,204 Thanks: 511 Math Focus: Calculus/ODEs Re: pi clock I used the IMG tags to display the larger image, and then removed the now unnecessary link to the image.
 January 18th, 2013, 06:32 PM #3 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233 Re: pi clock OH WOW! THIS IS SO COOL... where can i get one of these? [color=#008000]MarkFL[/color] , can you post the missing 1/4 picture?
 January 19th, 2013, 07:25 AM #4 Newbie   Joined: Jan 2013 Posts: 8 Thanks: 0 Re: pi clock I can not use IMG tag in my post. So here is the link to the picture above. http://www.sbcrafts.net/clocks/clock-pi.jpg
 January 19th, 2013, 09:17 AM #5 Senior Member   Joined: Nov 2010 From: Berkeley, CA Posts: 174 Thanks: 35 Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT Re: pi clock For the fifth position, I think that $\pi_1(\mathbb{S}^1)$ is the first homotopy group of the sphere. No idea about the seventh position, though.
January 19th, 2013, 10:05 AM   #6
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Re: pi clock

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 Originally Posted by Petek For the fifth position, I think that $\pi_1(\mathbb{S}^1)$ is the first homotopy group of the sphere. No idea about the seventh position, though.
I believe you are right and confirms I am on the right track. The S^^1 is a circle vector bundle. I read that the rank of a vector bundle is the dimention of its fibers. If raise to the 5th power, the rank then is 5. Cool.

 January 21st, 2013, 07:45 AM #7 Newbie   Joined: Jan 2013 Posts: 8 Thanks: 0 Re: pi clock I found the solution to the other question pertaining to 7 = |pi (sub 1), (L(7,3))|. The L in here is the least common denominator which is 21. The pi (sub 1) of (21) is the number of prime numbers except the first one from 1 to 21 which is 7.
 January 21st, 2013, 09:41 AM #8 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 Re: pi clock How about $\lceil \pi - \cos(\pi) \rceil= 5$?
January 21st, 2013, 12:23 PM   #9
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Re: pi clock

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 Originally Posted by Hoempa How about $\lceil \pi - \cos(\pi) \rceil= 5$?
cos(pi) is -1, ceiling of (3.14-(-1)) is ceiling of 4.14 = 5.

 January 22nd, 2013, 11:53 AM #10 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 Re: pi clock It was meant as a suggestion for your nice clock.

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