# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Wed, 22 May 2013 14:09:09 UTC

 All times are UTC [ DST ]

 Page 3 of 6 [ 78 posts ] Go to page Previous  1, 2, 3, 4, 5, 6  Next
 Print view Previous topic | Next topic

Pi
 is yummy 29% [ 11 ] is irrational 29% [ 11 ] makes your head ache 3% [ 1 ] makes you wonder 39% [ 15 ]
Author Message
 Post subject: Posted: Tue, 15 Mar 2005 04:03:20 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 7 Nov 2004 08:21:37 UTC
Posts: 2987
kippah wrote:
bugzpodder wrote:
its the circumference of a unit circle, thats how it is defined.

pi is half the circumference of the unit circle .. ?

Yeah.

cos 0 = 1
cos pi = -1 not = 1

Top

 Post subject: Posted: Tue, 15 Mar 2005 04:14:04 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Thu, 31 Jul 2003 12:36:00 UTC
Posts: 1737
unit circle has radious 1...if you consider the 'unit' circle to be diamater 1 then ...

Top

 Post subject: Posted: Tue, 15 Mar 2005 08:19:06 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 7 Nov 2004 08:21:37 UTC
Posts: 2987
heardie wrote:
unit circle has radious 1...if you consider the 'unit' circle to be diamater 1 then ...

This goes back to the original question then. Why do we use the diameter instead of the radius to define pi?

Surely, there's got to be a reason, right? Does it make a certain, important, class of equations easier? Because, the three cube roots of unity are:

1
e^(i*2pi/3)
e^(i*4pi/3)

Aesthetically, there's an extra factor of two hanging around...

Top

 Post subject: Posted: Tue, 15 Mar 2005 08:41:07 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 21 Feb 2004 09:22:14 UTC
Posts: 891
Location: Melbourne Australia
Factors of two are generally easier to work with than factors of 1/2, take one of my favourite results as an example:

Take out a 1/2 and you get which just looks ugly in my opinion.

It's a moot point really, I just don't think there's anything wrong with the current definition. Leave me be with my 2pi circumference

Last edited by kippah on Tue, 15 Mar 2005 08:50:45 UTC, edited 1 time in total.

Top

 Post subject: Posted: Tue, 15 Mar 2005 08:46:56 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 7 Nov 2004 08:21:37 UTC
Posts: 2987
kippah wrote:
Factors of two are generally easier to work with than factors of 1/2, take one of my favourite results as an example:

Actually, Mathematica 4 says that

But I guess you're right in that an extra factor of 1/2 is less pleasing than an extra factor of 2.

Arguably though, since 2 and 1/2 are such simple numbers, it doesn't matter too much. I was just curious...

Top

 Post subject: Posted: Tue, 15 Mar 2005 08:50:26 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 21 Feb 2004 09:22:14 UTC
Posts: 891
Location: Melbourne Australia
True, I'll edit my post. Fuzzy memory

Also

Top

 Post subject: Posted: Tue, 15 Mar 2005 19:01:08 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 15 Oct 2003 18:26:09 UTC
Posts: 1449
Location: The Sombrero Galaxy
kippah wrote:
True, I'll edit my post. Fuzzy memory

Also

Also,

Prove by induction . . .

Top

 Post subject: Posted: Fri, 22 Apr 2005 13:51:21 UTC
 Senior Member

Joined: Mon, 12 May 2003 20:32:25 UTC
Posts: 68
Location: London, UK
robert@fm wrote:
Such a pity that it's only Pi Day in North America. (Elsewhere in the world, where they use European or International date format, it's 14/3, not 3/14.)

I've just remembered that in countries which use European date format, Pi Day is the 22nd July (22/7).

Quote:
However, one can celebrate Pi Day by downloading the ZX-Spectrum* classic Pimania from World of Spectrum (along with an emulator if needed).  (Automata Software did a number of other Pi games, all of which are also there.)

*TS2068 in the USA.

The "date" portion of the solution to Pimania was 22 July, for the reason stated above.

Top

 Post subject: Posted: Fri, 22 Apr 2005 21:41:50 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
Kwyjibo wrote:
Hey Matthew!

Did you know that in 1899 the Indiana Legislature almost passed a bill
requiring that all Indiana schools teach pi to be exactly 4???

Wonder what the world would be like today if it had passed....

why 4!? It's closer to 3. Some people in government are just total morons.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: bump..Posted: Fri, 3 Mar 2006 21:25:31 UTC
 S.O.S. Oldtimer

Joined: Fri, 22 Jul 2005 05:23:58 UTC
Posts: 257
bump...

it's coming.

_________________

Top

 Post subject: Posted: Tue, 14 Mar 2006 04:02:33 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9632
It's Pi Day's Eve. Fun facts:

(1) Albert Einstein's birthday falls on Pi Day
(2) Pi Day is the same day as Steak and BJ Day, the males' answer to Valentine's Day
(3) Those of you not in America may instead celebrate the alternative: Pi Approximation Day

Top

 Post subject: Posted: Tue, 14 Mar 2006 14:07:16 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 6 Jul 2003 07:53:15 UTC
Posts: 409
Location: Melbourne, Australia

So can't you just 'factor' the n-fold integral and calculate it as or is that a fudge method?

Top

 Post subject: Posted: Tue, 14 Mar 2006 19:57:13 UTC
 S.O.S. Oldtimer

Joined: Fri, 22 Jul 2005 05:23:58 UTC
Posts: 257
HAPPY PI DAY!

_________________

Top

 Post subject: Posted: Tue, 14 Mar 2006 22:57:51 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 4 May 2003 16:04:19 UTC
Posts: 2906
Benny wrote:

So can't you just 'factor' the n-fold integral and calculate it as or is that a fudge method?

A similar identity:
http://www.sosmath.com/CBB/viewtopic.ph ... ar+algebra

_________________
Has anyone noticed that the below is WRONG? Otherwise this statement would be true:

where

Top

 Post subject: Posted: Tue, 14 Mar 2006 23:49:32 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 22 Jun 2003 18:00:06 UTC
Posts: 3461
Location: North TX
Matthew wrote:
It's Pi Day's Eve. Fun facts:

(2) Pi Day is the same day as Steak and BJ Day, the males' answer to Valentine's Day

you should have seen the look on mi esposa's face when I mentioned Steaks and a BJ ...

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 3 of 6 [ 78 posts ] Go to page Previous  1, 2, 3, 4, 5, 6  Next

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous