Pythagoras theorem

[arkain101]

pythagoras rule

 

[math]a^2 + b^2 = c^2 [/math]

 

 

 

A well known concept in mathamatics.

 

 

I was mapping out some shapes to understand why this was. In the process I drew out some shapes and saw something. I assume this not neccesaraly unknown.

 

The pythagoran theorem can be expressed as;

 

[math](2)a + (2)b = (4)c [/math]

[arkain101]

What got me interested in this was the physics aspects of nature.

 

The differential of distance(ds) in cartesian 3D space is defined as:

 

 

 

Which translates into.

 

[math](6)ds = (2)dx_1 + (2)dx_2 + (2)dx_3[/math]

[arkain101]

So I would predict that;

 

In the geometry of special relativity, a fourth dimension, time, is added, with units of c, so that the equation for the differential of distance becomes:

 

 

would translate into.

 

[math](2)ds = (2)dx_1 + (2)dx_2 + (2)dx_3 - (2)c(2)dt[/math]

 

Not positive..

[ughaibu]

Arkain101: Your formula only applies to isosceles triangles. Here's a page with "72 approaches to proving the theorem": Pythagorean Theorem and its many proofs

[ughaibu]

In fact, your formula doesn't work even for isosceles triangles.

[arkain101]

Okay what the heck..

I feel retarded now.

[ughaibu]

Dont worry about it. I think things like the Pythagorean theorem are great fun, simple but with incomprehensible ramifications.

[arkain101]

You know what I think I meant to be doing is this.

 

AB/BC = BD/AB and AC/BC = DC/AC.

 

 

If you see my drawing, that is what I was comprehending, of course thought I confused the maths by accident.

[arkain101]

What about this here?

 

Did I find a constant for squares? The hypotenuse of a right triangle with equal lengths for a and b, or the hypotinuse of a square is has a constant, 1.4142136....

 

[math]a^2 + b^2 = c^2[/math]

[math]5^2 + 5^2 = c^2[/math]

[math]5^2 + 5^2 = 7.0710678^2[/math]

 

Now,

 

[math] 1.4142136 \times length(a,b) = 7.0710678[/math]

 

Note Pie = 3.141

And the constant I found is 1.41

 

In other words the distance of a square corner to corner is;

 

[math] 1.4142136^2 = 2[/math]

 

Constant = [math]\sqrt 2[/math]

 

Sure hope I didnt make another blind mistake. :doh:

[arkain101]

:(

 

The length of the polygon diagonal of the unit square is [math]\sqrt 2[/math] , sometimes known as Pythagoras's constant.

[Turtle]

:(

 

The length of the polygon diagonal of the unit square is [math]\sqrt 2[/math] , sometimes known as Pythagoras's constant.

 

 

One can also derive this constant from the vesica piscis.

 

http://hypography.com/forums/physics-mathematics/1902-vesica-piscis-real-sacred-geometry.html