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Working in steel fab. shops, you build things that quite often need to be perfectly squared. I remember when my boss taught me the best way to square an angle perfectly. You measure 3" from the corner on one flange, 4" from the corner on the other flange and if the distance between the 2 marks is 5" then it is a perfectly square angle.
Can anyone give me the theorem that proves this? I just want to gain some understanding as to why this works.
~~Edited to fix tired retardedness.~~
I think what you meant was 3" and 4" (rather than 2" and 3" ;) ).
anyway.. it's the basic pythagorean triangle ( 5*5= 3*3 + 4*4 ).
It's simply the pythagorus (sp?) theorem, in one of the very few real-world situations I've heard of.
Goes for the multiples also : 6, 8 and 10 or 9, 12 and 15 ;)
Ðõèáãüñáò in Greek :)
Ope, yeah, I was tired as well when I typed out that question. I got it right in the title though. :D
Yeah, I thought it might be something like that. Thanks.
Search for “Pythagorean Theorem,” which proves that x2 + y2 = z2 if (x, y) are the short sides of a right triangle and z is the hypotenuse. I am pretty sure that the reverse theorem has also been proven.
The (3, 4, 5) triangle is the most commonly used one when a right angle is required. Similar triangles like (6, 8, 10) or (9, 12, 15) are often used to lay out the corner of a building because it is easier to get more precision with a larger triangle. Triangles with sharper angles like (5, 12, 13) or (7, 24, 25) could be used but are less convenient and likely to make precision a bit more difficult.
The following algorithm can be used to generate many Pythagorean triangles.(x, y, z) as defined above will always be a Pythagorean triple. If (u, v) have a common factor or both are odd, the resulting triangle will have sides with a common factor.
- Choose (u, v) such that u > v, (u, v) have no common factor, and one is odd while the other is even.
- x = u2 - v2
- y = uv
- z = u2 + v2
It may have few direct uses, but everything from vector algebra to the basic formulas of relativity are based on it.Quote:
Originally posted by si_the_geek
in one of the very few real-world situations I've heard of.