Know your numbers: 6.37

[Function]

Hello everyone

 

I have a rather odd question for you this evening.

 

Yesterday I posted a topic on the quadratrix (you should read it if you'd like to know more about it) and now I'd like to know if there's something special about the number 6.37, or a number that's really close to it, because, that's the place that the quadratrix of a circle with radius 10 intersects the x-axis...

 

I've tried using square root of pi, pi squared, square root of 10, and much more... I've even used the constant e...

 

But I can't to find an expression, using methematical constants and 10, which results in about 6.37...

The closest point I find is 2*pi...

 

Could someone help me in my search for the 'formula'?

 

Thanks!

 

Function

 

EDIT: Hmmm... I happen to find on a physics-like website (http://www.electronics-tutorials.ws/accircuits/average-voltage.html) that 0.637 would be [math]\frac{2}{\pi}[/math], so the intersectional point of the quadratrix would then be [math]\left(\frac{2r}{\pi},0\right)[/math]

Can anyone confirm this?

 

---

 

Alright, I've got another one for you: the area, included by the quadratrix and the right part of the square, divided by the area, bordered by the quadratrix and the left part of the square, equals about 1.27.

Anything special about this one?

Edited May 1, 2014 by Function

[Acme]

Wolfram|Alpha computational engine when input 6.37 gives the following as possible closed forms:

 

 

1/e~~6.367879

 

e^2-1~~6.389056

 

and

 

51/8~~6.3750000

 

Edit: D'oh! I missed the 'more' button. There must be a dozen such forms given. Here's one more interesting form that includes e & pi. (15 pi)/e^2~~6.3775249

 

Here's the link if you don't have this handy-dandy tool. >> http://www.wolframalpha.com/

Edited May 1, 2014 by Acme

[Function]

1/e~~6.367879

I doubt this It does mention sqrt(3)/e, however..

Keeping in mind that it does concern a circle, in some way, I think pi is more special here than e.

Edited May 1, 2014 by Function

[Acme]

I doubt this It does mention sqrt(3)/e, however..

Keeping in mind that it does concern a circle, in some way, I think pi is more special here than e.

Sorry; copy/paste error. Should read 6+1/e. See my edit of first reply too if you missed it.

[Function]

Sorry; copy/paste error. Should read 6+1/e. See my edit of first reply too if you missed it.

Don't sweat it. We're all human

Alright, numbers update:

 

A(circle)/A(quadratrix) = 1.780183697254104

 

p(circle)/p(quadratrix) = 1.268487635981663 (see the edit of my original post; how beautiful is it that it is the same?)

Edited May 1, 2014 by Function

[Acme]

Don't sweat it. We're all human

...

 

Alright, I've got another one for you: the area, included by the quadratrix and the right part of the square, divided by the area, bordered by the quadratrix and the left part of the square, equals about 1.27.

Anything special about this one?

What; me worry!? So I put your new number into the engine. It gave a dozen results again. I'll just give a couple and you can look at the rest there. (Have you used that tool before? She's a peach I tell ya! )

 

pi^2/8~~1.233700

 

pi^(1/5)~~1.257274

 

3-sqrt(3)~~1.267949

 

http://www.wolframalpha.com/input/?i=1.27

 

Edit: missed that A(circle)/A(quadratrix) = 1.780183697254104 edit. Found an interesting close-fit with e & pi for it. >> e^(1+e-pi)~~1.7801349

Edited May 2, 2014 by Acme

[Function]

What; me worry!? So I put your new number into the engine. It gave a dozen results again. I'll just give a couple and you can look at the rest there. (Have you used that tool before? She's a peach I tell ya! )

 

pi^2/8~~1.233700

 

pi^(1/5)~~1.257274

 

3-sqrt(3)~~1.267949

 

http://www.wolframalpha.com/input/?i=1.27

 

Edit: missed that A(circle)/A(quadratrix) = 1.780183697254104 edit. Found an interesting close-fit with e & pi for it. >> e^(1+e-pi)~~1.7801349

 

I know Wolfram|Alpha and she's just a beauty For 1.27, however, I can't seem to find any number that's 'special' enough to mention (except for pi/4, that's a special one, now, isn't it)..

The one you found for A(circle)/A(quadr.), however, is indeed very interesting!

Edited May 2, 2014 by Function