We did the same thing, just worded different. the first fomula shows the area of a square based on the length of side c is the same as the combined area of squares based on sides a + b.
the second fomula give you the lenght of side c. this works for all traingles, but if you use 3 and 4 as a muliplier, for a givin value, the length of side c will be muliplied by 5 to get a right triangle. I've used it alot to check how square the layout was for a large pattern. I think all my teacher alive or dead are rolling over on the ground or in their graves.
As pointed out in the introduction, if c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, Pythagoras' theorem can be expressed as the Pythagorean equation:
or, solved for c:
If c is known, and the length of one of the legs must be found, the following equations can be used:
or
The Pythagorean equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. A generalization of this theorem is the law of cosines, which allows the computation of the length of the third side of any triangle, given the lengths of two sides and the size of the angle between them. If the angle between the sides is a right angle, the law of cosines reduces to the Pythagorean equation.
Dave Patterson
odd_kins@yahoo.com
http://home.comcast.net/~oddkins/foundry_home.html
--- On Sat, 1/1/11, oldstudentmsgt <wmrmeyers@sbcglobal.net> wrote:
From: oldstudentmsgt <wmrmeyers@sbcglobal.net>
Subject: [gingery_machines] Re: new article: Making it Dead Flat and Square
To: gingery_machines@yahoogroups.com
Date: Saturday, January 1, 2011, 8:11 AM
David, that is supposed to be A-squared + B-squared = C-squared. If A=3 & B=4, C=25, as 9 + 16 = 25, and the square root of 25 is 5. It's called the Pythagorean Theorem, after the Greek philosopher who supposedly created it.
http://en.wikipedia.org/wiki/Pythagorean_theorem
The wiki article says the Babylonians knew of it, & used it, but didn't fit it into a mathematical framework. According to their article, Pythagoras arranged and prove it both mathematically and geomentrically, which is why he got the credit. LONG article... I just skimmed it.
No way around it. There WILL be math. ;) Even I cannot escape it, and if any of my teachers knew I had become a teacher, the living ones would drop dead, and the dead ones would start spinning in their graves!
Bill in OKC
--- In gingery_machines@yahoogroups.com, David Patterson <odd_kins@...> wrote:
>
> Egyptians knew about the 3,4,5 rule of a right triangle, simple geometry. If one side is 3 another is 4 then the hypotinus is exactly 5, for a right trangle. using a wheel of a known circumference a person can mark off an area if all 3 do not add up to this 3,4,5 rule it will not be exact.
> Â the formula is
> the square root of A(3)squared + B(4) squared = 5.
> Is the pyramid within 1/8" of a known dimension, doubt it. Is one side square within 1/8" to another, could be.
> Â
> Dave Patterson
> odd_kins@...
> http://home.comcast.net/~oddkins/foundry_home.html
>
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