Why is "Pythagorean Theorem" a Theorem and not a law.  It always works 100 % of the time?
108223
You are getting confused between the language in science and mathematics, I suspect. \n\nScience and mathematics are two different domains. They have their own terminology and cultures. Mathematicians want to call themselves scientists sometimes (although often not since that sounds too dirty and applied), but they are not. Scientists use mathematics, and sometimes the most theoretical scientists might even call themselves mathematicians, but they are not. Having worked in both mathematics and science, with plenty of each, I can definitely tell you that mathematicians are NOT scientists, and vice-versa. \n\nIn mathematics you can actually prove things. In science you cannot. You can have things that have a lot of evidence behind them in science, but no absolute proof like you can in mathematics. \n\nIn mathematics you have a set number of axioms that you agree on before hand (the rules of the game). In science you make assumptions sometimes, but it is often not as formal. \n\nIn science you have data from experiments. In mathematics you don't really have data, but you have calculations. \n\nIn science you have theories, and also in math you have theories, but they are not the same. Just like the meaning of theory in general use is not the same (much to the consternation and confusion of creationists, who just don't seem to get it, or at least want to get it). \n\nA mathematical theory like Group Theory will never be discarded because somehow someone has proved some new theorem and it is all obselete now. In science, the Theory of Gravity will eventually be replaced by something better that fits more of the data, although the previous theories might still be useful in some restricted domain.\n\nIn science you have models, which are somewhat like statistical models. Real mathematicians by and large will not touch a field as filthy as statistics. In science, statistics is just another tool.\n\nLaws are really something from science, not mathematics (although there is a cosine law in trigonometry; it probably should be called something else). And even the laws in science are not really set in stone like they are in mathematics. What science CALLS mathematical laws are really just models that sorta fit the data, kind of. More filthy statistics. However, I did find a few papers on the internet that did not call it the Pythagorean Theorem, but the Pythagorean Law. Hooke's laws, the Laws of Thermodynamics and the Law of Gravity are really not near as solid as the Pythagorean Law. Newton's Law of Gravity was replaced, and I am fairly sure that General Relativity will be replaced in turn, at least once more if not multiple times as more data accumulates. The meaning of the term "law" in common parlance is different yet again, just as it is in the case of theory. \n\nOne could continue with all manner of terms that sort of overlap between these fields, like lemma and corollary and hypothesis and conjecture and fact and error and converge and problem and experiment and prediction and data and so on. However, I think this serves to alert the careful reader to the fact that there are some linguistic and cultural minefields that have to be navigated with care.
1023328
Fermat's last theorem is that there is no solution in positive integers the the equation x^n + y^n = z^n, with n>2. \n\nThe above equation is different because some of the terms are raised to the 2nd power instead of the nth power. It is also different because it asserts an infinite number of solutions and Fermat's theorem asserts no solutions.
22351
Many have tried, yet none have found a formula. As noted on MathWorld,\n\n"Euler commented "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate" (Havil 2003, p. 163). In a 1975 lecture, D. Zagier commented "There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision" (Havil 2003, p. 171)."
1028326
1 - A is enough because with the lengths of 2 sides you can use pythagoras' theorem to work out the length of the other
180043
Umm....  there is no way to disprove it....thats why its called a law, not a theorem.  Also, you need to be more specific.  What ways?  Whats experiments?  \n\nAsk again with  more details and I will help you
169166
well i think yoru referring to fermats last theorem. This was proven by Andrew Wiles of Britan in 1994-1995.  He squestered himself in a room for more or less 7 years and came up with a solution.  Originally his proof was rejected when he first presented it in 1993 because an error was found.  He fixed the error and we now know that Fermats last Theorem is true.
164065
The trick with "proofs" like these are generally an obscured division by zero. One of the lines seems to work, though when you divide to cancel out some factors, the quantity you're dividing by could/does equal zero. It's a trick and doesn't say anything substantial about mathematics.
338816
As in many other pseudo-demonstrations of this kind, the error is to divide by zero (2-2) both sides of the identity. You can't do this because the division by zero is an undefined operation.\n\nFrom a well-known logic theorem, starting from a false statement, you can consistently derive any other false statement. This is the common source of many apparent paradoxes.
513181
First off, there is no such thing as a "natural law."  There are only natural events that always seem to happen when certain conditions are present.  The word "law" implies that the event must occur.  It would be better to ask: what is a mathematical expression of a "natural phenomenon?"  \n\nA list of many such expressions can be found at the link below.  Take your pick.
600012
My response is to use the pythagoras theory to answer the question. After all, the question was set for you, so it wouldn't be right to answer it for you, now would it?
288123
What the Pythagoras theorem states is that the square of the hypotenuse is equal to the sum of the squares of the two other sides (lets call them "a" and "b").\nSo you have to satisfy this condition:\n \nhypotenuse^2 = a^2 + b^2\n \nIn the case hypotenuse = sqrt(3),\n \n3 = a^2 + b^2\n\nSince there are an infinite amount of pairs (a, b) that satisfy this equation, there are infinite triangles.\n \nIf you´re thinking of the special cases (the ones you memorize for geometry and trig) I can only remember the case of sides 1, sqrt(2), sqrt(3). But I´m pretty sure there were 2 other cases (with different hypotenuses).
572376
You **did** say that the Pythagorean Theorem was a given, right? I think that your INTENT is to prove the converse of the Pythagorean Theorem, right?\n\nLet x, y, and z be positive integers such that\nx^2 + y^2 = z^2.\nClearly z > x and z > y (otherwise either x^2 or y^2 must be less than zero; prove this for yourself if you must).\n\nLet x and y be the sides of a right triangle that form the right angle.\nThen, by the Pythagorean Theorem the length of the hypotenuse h is\nh = √(x^2 + y^2)\nh = √(z^2) . . . . . . . . (given equation above)\nh = z . . . . . . . . . . . (given z is positive) \n        \nTherefore, by side-side-side congruence, any triangle whose sides are of lengths, x, y, and z, where x^2 + y^2 = z^2, must be a right triangle with hypotenuse z.\n\n\nASIDE TO HOOD...: You are using the Pythagorean Theorem to prove the Pythagorean Theorem. Although the questioner's intent is not perfectly clear, I don't think the intent was to prove "if x, then x". If so there are easier ways to do so.
1000630
Pythagoras Theorem asserts that for a right triangle with short sides of length a and b and long side of length c \na2 + b2 = c2 \n\nor c2-a2 = b2 \n\nhere is a link with all the necessary thing you have to know about this theorem . I hope it helps , just read it carefully and everything is going to be fine :)
726104
Pythagoras (of Samos, born about 569-82 BC - died about 507 BC) was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. \n\nIn any right triangle, the area of the square whose side is the hypotenuse (the long side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse, the adjacent and opposite in sine, cosine and tangent workings). \n\nIf we let c be the length of the hypotenuse and a and b be the lengths of the other two sides, the theorem can be expressed as the equation\n\nThis 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.\n\nI was taught this in a long jumpo sand pit, with 25 billard balls.\nmy old teacher, Mr Chadwick, made a line of 5 balls, and this was the hypotenuse. he then drew in the rest of the triangle. he squared the 5 balls, by making a square of 5 by 5 balls, (25 in all).\n\nthen he put balls on the other lines. three fitted onto the short side, and four onto the next side. he then squared the two other sides. 3 x3 and 4 x 4 (9 and 16, when added together = 25. \n\nhe showed me that 27 years ago, It was amazing, and the reason I am now a teacher.
1039593
A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.\n\nThe name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational.\n\nThere are 16 primitive Pythagorean triples with c ≤ 100:\n(3, 4, 5) (20, 21, 29) (11, 60, 61) (13, 84, 85)\n(5, 12, 13) (12, 35, 37) (16, 63, 65) (36, 77, 85)\n(8, 15, 17) (9, 40, 41) (33, 56, 65) (39, 80, 89)\n(7, 24, 25) (28, 45, 53) (48, 55, 73) (65, 72, 97)
652164
This theorem has an amazing number of proofs but this theorem(like many other mathematical concepts) as you said was known way before pythogorean times but only to INDIANS who didnt share it on the global scale!!
1112037
Pythagoras wasn't just a mathematician -- he was a cult leader, as well.  For more information, you could try a site like Wikipedia: