Somewhere around 1875 and 1876
I have to prove http://s5.tinypic.com/19ldma.jpg http://img22.imageshack.us/img22/9263/mathhlproofou4.jpg without using pythagorean theorem
Yes
The Pythagorean Theorem applies only to right triangles. (But they don't prove it.)
It does not.If you consider a right angled triangle with minor sides of length 1 unit each, then the Pythagorean theorem shows the third side (the hypotenuse) is sqrt(2) units in length. So the theorem proves that a side of such a length does exist. However, it does not prove that the answer is irrational. The same applies for some other irrational numbers.
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
James Garfield is the only president credited with an original proof of the Pythagorean Theorem.An educated guess is that most of the college educated presidents knew a proof of this theorem at one time in their schooling.
James A. Garfield
I have to prove http://s5.tinypic.com/19ldma.jpg http://img22.imageshack.us/img22/9263/mathhlproofou4.jpg without using pythagorean theorem
Yes
I don't think I could make the proof clear without a diagram, so you must check the related links to read it. I will say that it is algebraic in nature and is based on knowing how to find the area of a trapezoid. The first link is a student link and may not stay up for long. The second link contains several proofs of the Pythagorean theorem and you will have to hunt in it to find Garfield's proof, but it is there.
The Pythagorean Theorem applies only to right triangles. (But they don't prove it.)
For any right angle triangle its hypotenuse when squared is equal to the sum of its squared sides.
It does not.If you consider a right angled triangle with minor sides of length 1 unit each, then the Pythagorean theorem shows the third side (the hypotenuse) is sqrt(2) units in length. So the theorem proves that a side of such a length does exist. However, it does not prove that the answer is irrational. The same applies for some other irrational numbers.
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
James A. Garfield
Because in a right angle triangle the square of its hypotenuse is always equal to the sum of each side squared.
Yes, the corollary to one theorem can be used to prove another theorem.