Irrational Pi Defrocked

[MortenS]

I'd like you to get back to the regular polygons circumscribed and inscribed on a circle, Robust.

 

I found a web-site that illustrates nicely what I tried to convey to you earlier. It regular polygons (3-100 sides) inscribed in a circle.

 

Pull the slider to the right, and watch how the perimeter of the polygon approaches that of the circle:

http://argyll.epsb.ca/jreed/math9/strand3/polygon_area_per.htm

 

 

Try to divide the perimeter of the polygons on 2*radius aas you increase the number of sides in the polygon, and you will see that the ratio will get closer and closer to pi. Now imagine what will happen if you increase the number of sides even more....

 

I cannot vouch for the results used on that webpage, but if you agree that if there is a general method to calculate the perimeter of an n-sided regular polygon, you have to agree that as n increases, the closer the perimeter will approach the circumference of the circle. Dividing the perimeter of the polygon with the diameter of the circle will give approximations to pi, with increasing accuracy as the number of sides increase.

 

Incidentally, this method of approximating pi was first used by Archimedes.

 

http://departments.weber.edu/physics/carroll/Archimedes/pi.htm

[C1ay]

I don't even know what you mean by a prime number, Clay....other than one divisible by no number but itself or unity - the latter invoking an interesting discussion we might take up somewhere down the line. More to the point here - I sense that you are purposefully attepting to confuse the topic by your obviously superior maths knowledge. No need to - obviously you da man!!

No one's confusing anything here. You've made the unsubstantiated claim that you can find the radius of a circle using any value for pi that you want and you've claimed unsubstanially that the area of a closed continuum must be given by a finite number. Now it's time for you to show us your proofs.

[Qfwfq]

I have no idea what you just said, Qfwfg. There must be a more straightforward prime number.

How 'bout 2? How 'bout 3?

 

There are infinitely many primes, exactly as many as naturals, take your pick. :circle:

[quantum quack]

maybe a little off topic but I thougth it might be of interest to post these two pictures.

 

A friend ran a program that compliled the pictures in grey scale using pi as a source for the left one and a random number generator for the right one. Each digit value 0 - 9 being given a grey scale colour.

 

The reason for the generation was to compare the lack of patterns in pi and the supposedly natural patterns of the random.

 

It is interesting to note that pi seems to allow for the greatest diversity, which suggests that diversity is a natural function and outcome of curved spacetime.

 

NB, if you want I will delete this post. Just thought it might be of interest.

[Robust]

maybe a little off topic but I thougth it might be of interest to post these two pictures.

 

A friend ran a program that compliled the pictures in grey scale using pi as a source for the left one and a random number generator for the right one. Each digit value 0 - 9 being given a grey scale colour.

 

The reason for the generation was to compare the lack of patterns in pi and the supposedly natural patterns of the random.

 

It is interesting to note that pi seems to allow for the greatest diversity, which suggests that diversity is a natural function and outcome of curved spacetime.

 

NB, if you want I will delete this post. Just thought it might be of interest.

 

Interesting indeed, and thank you for that. The diversity evidenced of space/time curvature as we might expect it to be.

[Kirk Gregory Czuhai]

those two patterns are INDEED INTERESTING, in those graphs!!!

love and peace,

and,

peace and love,

kirk

[quantum quack]

it is also interesting to note that teh picture of pi is row by row left to right progressing downwards.

 

a pic was generated which i don't have copy of that was circular from the center outwards and the results appear almost identicle.

 

it seems that no matter how you format the graphing pi always refuses to show a pattern.

Although this may be a premature statement.

BTW the total number of digits used in the pic was 250,000 if I remember correctly.

[Qfwfq]

How about trying that for various roots of various prime numbers?

 

I doubt you would find more difference than there is between these pictures.

 

Side question: what algorithm were those "random" numbers generated with?

[quantum quack]

How about trying that for various roots of various prime numbers?

 

I doubt you would find more difference than there is between these pictures.

 

Side question: what algorithm were those "random" numbers generated with?

Q, unfortunately the information you seek was lost in a recent server computer crash.

The whole question came up in a discussion on Pi being a ceature of diversity and how it goves teh impression of diversity by design when in fact it is simply diversity by necessity. In fact it was considered that the universe could only have succeeded in existing becasue of the nature of curvature or spheres, or circles...etc....

the pic was a very quick response to the idea of showing pi in some sort of pictorial form. i am sure someone with a bit of time could do a better job of it....

 

I must admit the thing that amazed me when i saw it for the first time was how similar it appeared to our night sky on a reeally clear night. The star scape seemingly to be an emulation of the necessity of pi, and it's seemingly continuous infinite resolution.

 

there are also websites devoted to the golden ratio which i can't say i know that much about.....facinating depictions. i will try and find a link......

The handle of person who generated the pic for me, was lost in the sever crash so i can't even contact him.