2007-10-17 05:40:47 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Simple, intuitive and logical solution to a problem.
2007-10-17 06:01:19 · answer #1 · answered by ib 4 · 0⤊ 0⤋
An elegant procedure is not the same as an elegant formula or equation. Procedure refers to process and in mathematics we use a process to prove that a conjecture is true or to solve a problem.
An elegant procedure is a proof or solution that is clear to all initiated reader, accepted as correct, has a readable and interesting style, and uses as few steps as possible without sacrificing clarity.
A solution such as 2x -3 = 7 = 10 = 5 ends with the correct solution of 5 but contains untrue statements such as 7=10, and is not clear. Solutions that just show answers or a few intermediate steps are not elegant because they do not show the thinking process that went on to arrive at the solution.
An elegant procedure in a proof or solution clearly states what assumptions are being made, what is to be proved or found, and the procedure followed to establish the proof or arrive at the solution is clear (the logic and methods used are either stated or generally accepted by those who work at that level of mathematics) and concise (nothing extra that is unnecessary for the proof or solution is used).
Solving the equation 7x^2 = 70x - 175 by the quadratic formula would not be elegant though it would produce the correct solutions.
Recognizing that the above equation can be divided by 7 and then factored into (x-5)^2 = 0 with solution x = 5 is elegant since it avoids the large and cumbersome numbers produced by the quadratic formula by noticing the common factor 7 in each term can be cancelled to give a perfect square which is easily factored.
Reading a problem carefully and thinking about a strategy before starting will usually produce a more elegant proof or solution than just jumjping in a trying whatever comes to mind first.
2007-10-17 13:08:17 · answer #2 · answered by baja_tom 4 · 1⤊ 0⤋
My favorite and, I think, the most beautifully elegant one is:
e^(iÏ) +1 = 0
The equation connects the four major branches of mathematics: arithmetic, algebra, geometry, and analysis.
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2007-10-17 12:45:20 · answer #3 · answered by Robert L 7 · 1⤊ 0⤋