Excuse Me While I Drill A Hole My Head

In summary, the conversation discusses various methods for calculating pi, including the use of trigonometric functions and infinite series. The true meaning of pi is also debated, with one person arguing that it is simply the ratio of a circle's circumference to its diameter, while others suggest using different mathematical approaches to find it. Ultimately, pi is described as a fundamental number that can be found through different techniques, including inscribing polygons in a unit circle and using a Monte Carlo method.
  • #1
eNtRopY
Maybe I'm a little slow, but the true meaning of pi just occurred to me.

tan(pi/4) = 1

arctan(x) = [sum]n=0[oo] (-1)n * [ x2n+1 / (2n + 1) ]

pi = 4 * arctan(1) = 4 * [sum]n=0[oo] (-1)n * [ 1 / (2n + 1) ]
= 4 * ( 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... )
= 4 * ( 2/3 + 2/35 + 2/99 + ... )
= 4 * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...]

Remember the equation for the area of a circle.

A = pi * R2
= (2*R)2 * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...]
= D2 * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...]

Now, draw a circle with diameter D. In that circle, place a square with area (2/3)*D2. Notice that there is still some empty space left on the sides square (where the square and the circle do not both exist). Place four squares with area 1/70*D2 in each of these four empty spaces. Continue to fill up the unoccupied space of the circle with progressively smaller squares ad infinitum.

Pi is simply an infinite series sum of scaling factors needed for filling a circle with squares in order to perform a numerical integration method.

eNtRopY
 
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  • #2
Pi

Its a bit more complicated, or simple really., glad to see someone else has found the Antiqity Keys to the Universe!

There is an obvious scaling factor, and when you invert the 'outside'square into the 'inside' circle, then the dimensional scale is maintained!

http://groups.msn.com/Youcanseehomefromhere/consciouswaves.msnw [Broken]

The movement, or transition from a Square to a Circle in '2-dimensions
', involves the inversion of area external to internal.

Below is representative of such an invertion:


http://groups.msn.com/Youcanseehomefromhere/consciouswaves.msnw?action=ShowPhoto&PhotoID=54 [Broken]

And the hidden relationships of interconnective Pi and geometric shapes can be clearly seen, as the shape expands, it expands to precise geometric formulas.

Click on the image for a larger pic.

http://groups.msn.com/Youcanseehomefromhere/consciouswaves.msnw?Page=2 [Broken]
 
Last edited by a moderator:
  • #3
Originally posted by eNtRopY
Maybe I'm a little slow, but the true meaning of pi just occurred to me.

Well, yeah that's a neat way to get pi, but excuse me if I am wrong isn't the true meaning of pi the ratio of a circles circumference to it's diameter? I think the most simple and elegant way to find pi is to just inscribe a polygon inside a unit circle, we know how to find the length of the sum of the sides of the polygon so pi is the limit as the number of sides goes to infinity. This is what makes the most sense to me. But there are many various other ways to get it. The two others that I like best are Wallis forumula and a monte carlo method where you have a unit circle inscribed inside a unit box and then you start randomly dropping points inside the box and can get pi as a ratio of the number of points inside the circle versus the total number of points (this ones fun to see a computer program do, the applet I saw do it also had a timeline above it which showed what the current value of pi was and how it changed in time as you added dots, it was neat to see it converge very quickly and accurately to pi!)
 

1. What is "Excuse Me While I Drill A Hole In My Head"?

"Excuse Me While I Drill A Hole In My Head" is a popular phrase used to express frustration or exasperation. It is not a literal action of drilling a hole in one's head, but rather a figurative expression.

2. What is the origin of the phrase "Excuse Me While I Drill A Hole In My Head"?

The phrase is believed to have originated from the 1967 song "Hey Joe" by Jimi Hendrix, in which he sings "Excuse me while I kiss the sky." It has since evolved into the commonly used phrase "Excuse me while I drill a hole in my head."

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The phrase is used to convey a sense of frustration, anger, or annoyance. It can also be used to express a feeling of being overwhelmed or at a loss for words.

5. Can the phrase "Excuse Me While I Drill A Hole In My Head" be used in a professional setting?

No, this phrase is considered informal and should not be used in a professional setting. It is best suited for casual conversations with friends or family.

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