[RESOLVED] Pythagoras and I

[BillGeek]

Hi All

Yet again, my basic mathematical skills (non-existent now) has failed me. I'm trying to apply the theory of pythagoras from a different perspective. Given the following, how would I be able to calculate x / y?


x = y

So this is where I get stuck:

r^2 = x^2 + y^2
... 1^2 = x^2 + y^2
... 1 = Sqrt(x^2 + y^2)

See the problem, or am I just having one of those days again?

Any help would be appreciated!

[zaza]

Fill in x = y....



But surely if x = y, then x/y = 1...?

[BillGeek]

Nope. If you say x and/or y = 1 then:

r^2 = x^2 + y^2
Therefore: 1^2 = 1^2 + 1^2
Which means: 1 = 1 + 1...

[03myersd]

Right lets start from scratch.

R = 1 and it is the hypotenuse
y = x

So R^2 = y^2 + x^2

Since y = x: R^2 = x^2 + x^2 = 2x^2

R^2/2 = x^2
Sqrt(R^2/2) = x

x = Sqrt(1^2/2)
x = Sqrt(0.5)
x = 0.71

Since x = 0.71 then y also = 0.71

Hope this is clear enough.

[TheBigB]

table-wise

Step 1: Enter given values (hypotenuse = c)

      x  |  x²
    -----------
  a      | 
  b      | 
    -----------
  c   1  |  1
  

Step 2: Split the 1 and Squareroot it.

      x  |  x²
    -----------
  a  0,71| 0,5
  b  0,71| 0,5
    -----------
  c   1  |  1

[BillGeek]

03myersd Nice one!

So in theory... whenever X = Y, you will have:
x = Sqrt(r^2/2)

EG:

Say X = 4 and X = Y

x = Sqrt(r^2/2)
Therefore: 4 = Sqrt(r^2/2)
Therefore: 16 = r^2/2
Therefore: 32 = r^2
Therefore: r = 5.656

Original Theory:
r^2 = 4^2 + 4^2
Therefore: r^2 = 16 + 16
Therefore: r^2 = 32
Therefore: r = 5.656

Interesting...

Thanks guys! A lot of help!!!

[zaza]

Nope. If you say x and/or y = 1 then:

r^2 = x^2 + y^2
Therefore: 1^2 = 1^2 + 1^2
Which means: 1 = 1 + 1...

I think you'll find that "x/y" is terminology for "x divided by y" which is why, if x = y, x/y = 1.


But before 03myersd spoilt it, I was trying to prod you in the direction of realising that x = y and filling it in to your equation...



Incidentally, regarding your last point, when the X and Y legs are equal then the corner angle must satisfy tan A = 1 - i.e. A = 45^o. Since this is the case, then all such triangles are similar, and the sides just scale.

[03myersd]

Correct!

[zaza]

...and BillGeek was originally asking how to calculate x/y....

[BillGeek]

I think you'll find that "x/y" is terminology for "x divided by y" which is why, if x = y, x/y = 1.

Sorry, I did not realize it. I thought it was "x or y"...(Perhaps that's why I had horrible marks for maths )

Thanks for the help you guys!