Re: [RR] Let's take a test-ANSWERS

[clint grant]

I think the key to this folly is the statement you made: "according to several websites". Which, among several tens of thousands on any given subject, one should have no problem finding a few (or several) which contain less than accurate historical information. The case still remains that there are the two distinct methods of finding the solution to the problem, which was and still is the original point of contention brought up by you, and which seems to have fallen to the wayside in your most recent discourse, quite understandably. (You simply had no other leg to stand upon.) This was , and still is, where you are mistaken. The two methods are not the same.    For instance, take a right triangle with two legs  of 7" and 20" and x" as the hypotenuse. The 3-4-5 method will not be applicable in this case, but the pythagorean theorem will. 7x7=49 20x20=400. 49+400=449  square root of 449=21.18962" - the hypotenuse.   The most widely accepted view is that Pythagoras is credited with the theorem which is named after him. In fact, this is the first time I have actually heard of anyone attempting to contest that. My source, for the sake of time and convenience, shall be :   Funk and Wagnalls Standard Dictionary   Under the definition of the word:   Pythagorean theorem (pi THag e REE en) Geom. the theorem of Pythagoras that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.   What seems to have occured here, both in your supposition and in your subsequent website research, is a confusion of the Pythagorean theorem and the 3-4-5 method. While the Pythagorean theorem will apply in the 3-4-5 case, as it will in any right triangle, the 3-4-5 method depends upon triangles with multiples thereof, providing further proof both of the distinctiveness of the two methods and the falseness of your original claim that they are the same.   BTW, the most widely accepted view by historians is that the egyptians developed the 3-4-5 method for use in the cornfields. No need for me to reference that, it's just simple common knowledge that I've been aware of since high school geometry, and that will stand on it's own merit.  Myself, I think Job came up with it, but that's another story.     ----- Original Message ----- From: [EMAIL PROTECTED] Sent: Sunday, February 24, 2002 10:16 PM To: [EMAIL PROTECTED] Subject: Re: [RR] Let's take a test-ANSWERS   And a 3-4-5 triangle is simply the smallest integer right triangle known where the area is also an integer namely (6 Square Units). Right triangles having integer (whole number) sides are known as "Pythagoran Triangles". Besides,  according to several websites the actual origin of the 3-4-5 right triangle is most likley unknown. This means that whom ever first discovered or comprehended the 3-4-5 right triangle's existence has no historical reference as to the place, time, and circumstances of its discovery. The discovery of the 3-4-5 right triangle was probably known some time before 1900 BC to 1600 BC. The Babylonians were the first to document the existance of the 3-4-5 right triangle and several other integer sided right triangles as recorded on a Babylonian Clay Tablet known as "Plimpton 322" using cuneiform script made by pressing styles into moist soft clay. The statement of the Theorem was discovered on a Babylonian tablet circa 1900-1600 B.C. (the same tablet mentioned before). Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. Pythagoras didn't discover the theorem - he simply proved it.  One of Pythagoras's proofs included the 3-4-5 triangle.  Multiples of that, such as the ones you listed, are the same. 2/24/2002 12:38:23 PM Pacific Standard Time, [EMAIL PROTECTED] writes: No, you are mistaken. These are two diferent methods. Pythagorean theorem is as I stated. Pythagoras was a greek mathematician. His theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. A squared +b squared = c squared. The 3-4-5 method states that a triangle with sides divisible by 3, 4, and 5 respectively will always be a right triangle. The egyptians came up with this one for planting straight rows of corn, and I used it many times to build square houses, as recently as last week. Try it. 3,4,5,-15,20,25- 6,8,10-etc. Get more from the Web. FREE MSN Explorer download : http://explorer.msn.com