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You are not logged in. #1 20121222 10:04:39
Creating Functions?Okay hopefully this doesn't make me look incredibly stupid, but this is my problem. I'm wondering how mathematicians come up with their formulas. For an example, I ran into one of those pictures where it asks you how many squares are inside the other square  and instead of counting them I wanted to find out how to create an equation that would solve the problem. So say the square is a 4x4 square(one big square made up of 16 smaller squares. I attempted to try to figure an equation...well what I came up with was a function that would solve the problem, but only if you knew what the previous function was, as in: #2 20121222 15:57:38
Re: Creating Functions?One approach: Work out lots of cases and examples and look for patterns that can be turned into Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #3 20121222 16:08:49
Re: Creating Functions?Hi therussequilibrium; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20121222 16:45:21
Re: Creating Functions?bobbym  Last edited by therussequilibrium (20121222 16:47:24) #5 20121222 16:48:39
Re: Creating Functions?Hi; for your answer? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121222 16:50:03
Re: Creating Functions?Yes, that's what I meant, not sure why I put f(x)^2 at the end, I just mean x^2. #7 20121222 17:02:53
Re: Creating Functions?Hi; Did you check that against the other formula? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20121222 17:03:56
Re: Creating Functions?Just noticed the math function that we could use, so sorry about the ugly looking equations before. Yes, that's correct. #9 20121222 17:05:49
Re: Creating Functions?Yes, they are the same pattern, they both solve the square question  but to use my equation you have to know what is equal to, so it seems incomplete.#10 20121222 17:08:31
Re: Creating Functions?That is not correct, yours is a recurrence. You only needed to know f[1] to prime it all the rest come from that. That is an excellent way to solve the problem! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20121222 17:09:45
Re: Creating Functions?I would love to, because the only way I can possibly see how to is go through and manually figure them all out, which could take days if the square is a really large one lol. #12 20121222 17:13:01
Re: Creating Functions?Actually a recurrence is quite fast to do with a graphing calculator or a computer and is somethimes the preferred way. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20121222 17:15:26
Re: Creating Functions?Thank you, I really appreciate your help in this. #14 20121222 17:29:07
Re: Creating Functions?Do not appreciate it yet. This will be tough to understand at first. So we have our first formula: In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20121222 17:49:40
Re: Creating Functions?Yep, a little confused. I see that I'm just not sure where that equation came from, it looks a lot like the equation they found to solve the square problem. #16 20121222 17:53:50
Re: Creating Functions?That is the equation just in a different form. The summation calculus is like the integral calculus. Only it is for the discrete not the continuous. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20121222 17:58:39
Re: Creating Functions?Ahh, okay, I see it now  just not completely sure what happened on the second step, but I do see that the final equation equates to the original. #18 20121222 18:09:55
Re: Creating Functions?Hi; We form the collocation equations. We know from the recurrence that n = 1, f(n) = 1 n = 2, f(n) = 5 n = 3, f(3) = 14 n = 4, f(4) = 30 So just plug in to the avove equations and solve for a,b,c,d we solve that set: In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20121222 18:18:29
Re: Creating Functions?Okay, now that's awesome, but how did you guess the pattern was in the form of ? Is this a well known equation that I don't know?#20 20121222 18:22:09
Re: Creating Functions?The third method, tells us the the answer is a cubic. Also even if you can not do the summation in the first method you know that the integral ( almost like the sum ) of an x^2 involves an x^3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20121222 18:28:08
Re: Creating Functions?I'm ready, I'm writing this all down so I can study it and get a better grasp of it all. #22 20121222 19:00:51
Re: Creating Functions?Alright, no worries, I appreciate you taking your time out to help me  so take all the time you need. #23 20121222 19:04:45
Re: Creating Functions?I want to point out that I am just showing ways to solve your recurrence. We have not examined if there was an easier way to solve the original problem besides the recurrence. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #24 20121222 19:17:13
Re: Creating Functions?I understand, this information is still very helpful to me. It's obviously showing me there is a lot I need to learn; I'm a freshman in college and I really want major in mathematics, but from your general knowledge and understanding it would seem that I'm extremely far behind and I'm not sure I can catch up. So, this helps a bit... #25 20121222 19:20:37
Re: Creating Functions?Everyone can catch up. In my country there is a growing feeling that to learn math you need special talents. Other countries I am being told believe that it is just a matter of hard work and desire.
This one uses differences and a formula. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 