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May 19th, 2018, 07:48 AM   #11
Math Team
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,314
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I emailed this (about 15 years ago) to someone on the Internet who
wanted opinions on the stupidity of these mathematicians who keep
calculating PI forever and ever. (at bottom is a little true anecdote
between me and a wise older friend, Mason Johnson).
.................................................. ...............................................
Hi. Well, they remind me of the guy who spent years sticking together
over a million matches to come up with a miniature 'London Bridge':
got queer looks, some respect for his tenacity...but only 5 bucks at
the corner pawnshop....

This stupidity seems to have started in England (where else!) in the
early 1900's. A British mathematician William Shanks worked it out to
707 decimal places doing calculations by hand...over 20 years. POOR
BILL: an error in the 528th place was discovered in 1945...wonder if
they changed the inscription on his tombstone.

In Aug/89,YASUMASA KANEDA carried PI to 536,870,000 places, filling
110,000 pages of computer paper taking 67 hours and 13 minutes on
Japan's fastest supercomputer. ...gee, I would have bet my 20 against
your 10 that some Chineese fellow would have done this...doesn't the
rumor say they're the, every respectable computer store
has one constantly working on a computer keyboard, all visible from
the front store window.

Did a search on PI the other day: they're proudly announcing the
crashing of the 2 billion mark...WOW-WEE.

Purpose: make Pi=3.14 even.
First, let's use a circle of diameter 12 inches.
Next, let's use 3.14159 as 'the going' PI.
3.14159 x 12 = 37.699 inches.
3.14000 x 12 = 37.680 inches.
Difference: .019 of an inch (about thickness of 4 sheets of paper).

So, after drawing your 1-foot-diameter-circle, all you need to do is
make 4 little nicks of .00475 inch (.019/4)(thickness of one page) at
each 90 degree and no one will ever know....

DENIS AND MASON (a keep-it-simple wise elderly friend)
DENIS: Hey Mason, just decided to take this amazing course.
MASON: Ya? What's it called?
DENIS: The Sylva Method of Mind Control.
MASON: Hmmm...what will you learn there, Denis?
DENIS: Amazing things, Mason; I'll be able to control my own mind and
make it do all sorts of things.
MASON: Well...can you give me a couple of examples?
DENIS: Sure. At the demonstration, they told me I'd be able to figure
out what my dog is thinking; also, when I get a letter in the
mail, I'll hold it at both ends with my fingertips, concentrate,
and I'll be able to tell what is in the letter...imagine that!
MASON: Gee. Tell me, Denis, how much is this course costing you?
DENIS: Only 325 bucks, Mason.
MASON: Well, why don't you buy yourself a plastic letter opener instead:
only 79 cents at K-Mart....

NOTE: Fortunately, refunds were allowed before the 1st official lesson!!
Thanks from JeffM1
Denis is online now  
May 19th, 2018, 10:01 AM   #12
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Joined: Sep 2015
From: USA

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&\lim \limits_{n \to \infty} \dfrac n 2 \sin\left(\dfrac {2\pi}{n}\right) = \\ \\

&\lim \limits_{n \to \infty} \pi \dfrac{\sin\left(\dfrac {2\pi}{n}\right)}{\dfrac{2\pi}{n}} = \\ \\

&\pi \lim \limits_{n \to \infty} \dfrac{\sin\left(\dfrac {2\pi}{n}\right)}{\dfrac{2\pi}{n}} =\pi


Where the limit evaluation comes from the well known fact that

$\lim \limits_{x\to \infty} \dfrac{\sin(x)}{x} = 1$

So yes. This magic number is indeed a sort of $\pi$ and reaches it in the limit
Thanks from Denis and JeffM1
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May 20th, 2018, 08:13 AM   #13
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Beer soaked opinion follows.
Originally Posted by Forummur View Post
You really gave him an excellent answer using that formula involving the radius and sin(2pi/n) which I wasn't aware of. Also, in general as you probably know there is a simpler formula to determine the area of any regular polygon if you know its perimeter (p) or the length of each side and the length of an apothem (a) where an apothem is the perpendicular length from the center of the polygon to each side. An apothem is the same as the radius of a circle inscribed in the polygon whereas a radius of a polygon is the same as the radius of a circle circumscribed around the polygon. Anyway the apothem-perimeter formula is Area = (1/2)ap.
Simpler perhaps but I somehow prefer romsek's analytic/trigonometric approach.
It feels easier to recreate without consulting a textbook especially when you've forgotten more than half of what you've learned from plane geometry. You just sketch the unit circle and voila; everything seems clear.
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May 29th, 2018, 08:22 AM   #14
Joined: May 2018
From: Idaho, USA

Posts: 24
Thanks: 3


I’m sorry I have not been a long time, I had some really rough things happen.

I was looking at everybody’s equations they recommended. I did a little experiment, and I tried your equations. I also did an equation that I told you about earlier that I made up, which is 2.37765r^2.

After doing all your equations, and mine, I realize that we are all right. All these equations, even mine, get the same answer.

If there was a mixup, I apologize.

Thanks for helping me out with the formulas.

jnicholes is offline  

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