mm-1025 === Subject: Re: Integration of natural log integration of natural log the inverse function of e^x is going to be Inx. so if we have the inside the e^x graph rather than area under the curve, i think it should answer the question. so Inx is going to be the y function. the area of the rectangle is going to be xInx. the area outside would be /Inx e^xdx so e^[Inx]=x shaded portion outside would be area of x. /low so the rectangle area minus this area would be xInx-x and the antiderivative being xInx-x+C === Subject: Re: Pells eq. algorythms by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBJNufr12783; >Hi Todd, >Well, I apreciate very much your answer. Sure. Well, it was my pleasure. >I observed the diference in the notation : I used A and you use D Makes no difference. >I think this is coming from the the books we studied. Well, my solution comes from my own playing around with the problem, not from books. Although I have read a few in my life :) >Did you ever tried or see the cyclic method used in India back in 800 >A.D to find the solutions? No, but it sounds interesting. Why dont you tell us about it? The word cyclic reminds me of the fact that the integers which pop out of the continued fraction method are palindromic (e.g. 2, 1, 1, 1, 2 in my example). >Did you wonder If Archimedes had a method to solve the eq. when in >theCatlle >story- problem he get us to resolve a Pells equation at the end of >calculations? I seem to recall reading something about this in the American Mathematical Monthly some years ago. I recall the discussion was very interesting and maybe Ill dig it up and reread it, now that you bring it up. >Did you ever wonder what was Fermats method to resolve it? Well, I havent studied Fermat. I have the impression that he used his method of descent to solve a great many problems, and I half-expect youll be telling me something more about this. >Well , I know,in this Age we are conditioned to be very pragmatic, >learn to use a method well and be able to Aply it.So less and less we >dont have time to wonder >or find diferent ways to resolve a problem. Use of words like conditioned, or imputations that people (like me, presumably) dont wonder any more, are rather obnoxious and presumptuous, dont you think? If you want to have a discussion, then you should really be more polite, my friend. >I think you are very nice for writing down for me the use of continuu >fractions in this > case ,but I was looking beyond this when I put the question.I mean,I >wanted to hear some original coming from Wondering. down something I knew, thinking it was a real question (and not some sort of challenge, which is how it looks to me now). Ill try to be more careful next time. >Yes, You gave me the case D=61.In one day,two,three days from now I >can show to you my algorythm which I call Fermats algorythm.Well >,this algorythm is much simple than what your preference(my >opinion).This algorythm shows how Fermat used it to proof his >staments about representations of different primes too. >In another words it opens a Window in the Hystorie of past methods Well, great! Im always pleased to learn new things. I do think the method I gave is pretty simple, and I suspect that at some level other solutions are in some sense equivalent, but Ill wait to hear more from you. >Remember, Euler was a master of Algorithms and he fail to find one for >Pellequation >Some Professors know about this method because I PUT IT OUT ,I have >shown it to > them in writting.But you have to show to me that you look a little >bit in the Hyistory of mathematics.Take a course If you did not or >studied it by yourself. >It is fascinated and insight inspiring.That if you like mathematics . Well, I congratulate you on your successes with Professors, but... I have to show you *what*? I congratulate you further -- youve got quite a lot of nerve. Todd Trimble === Subject: computing the logarithm of arbitrary base hey folks, silly question from someone who prolly never should have embarked on a 3 year bachelors degree in mathematics... anyway, i would like to compute the b-base logarithm of a number, but my calculator seems only allow me the bases e and 10... hints anyone?? thnks === Subject: Re: computing the logarithm of arbitrary base > hey folks, silly question from someone who prolly never should have embarked > on a 3 year bachelors degree in mathematics... anyway, i would like to > compute the b-base logarithm of a number, but my calculator seems only allow > me the bases e and 10... hints anyone?? Learn mathematics, ditch the stupid calculator. Have any of them ever passed a math class? Stick with them and youll be doing the same. === Subject: Re: computing the logarithm of arbitrary base > hey folks, silly question from someone who prolly never should have embarked > on a 3 year bachelors degree in mathematics... anyway, i would like to > compute the b-base logarithm of a number, but my calculator seems only allow > me the bases e and 10... hints anyone?? To convert logs from any acceptable base Ôa, log_a, to an acceptable base Ôb, log_b: log_b(x) = log_a(x)/log_a(b) The acceptable bases are positive and not equal to 1. === Subject: Re: computing the logarithm of arbitrary base > hey folks, silly question from someone who prolly never should have embarked > on a 3 year bachelors degree in mathematics... anyway, i would like to > compute the b-base logarithm of a number, but my calculator seems only allow > me the bases e and 10... hints anyone?? > Learn mathematics, ditch the stupid calculator. Sure. I have a old CRC math tables book around here somewhere. > Have any of them ever passed a math class? > Stick with them and youll be doing the same. === Subject: Re: computing the logarithm of arbitrary base by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKJVlS13217; Richard Henry http://mathforum.org/epigone/alt.math.undergrad/slegomglu > hey folks, silly question from someone who prolly > never should have embarked on a 3 year bachelors > degree in mathematics... anyway, i would like to > compute the b-base logarithm of a number, but my > calculator seems only allow me the bases e and 10... > hints anyone?? >> Learn mathematics, ditch the stupid calculator. >> Have any of them ever passed a math class? >> Stick with them and youll be doing the same. > Sure. I have a old CRC math tables book around here somewhere. It wont help the original poster, though. I have the 20th edition in front of me right now. Common Logarithm Tables -- pp. 186-209 Natural Logarithm Tables -- pp. 210-217 Logarithms to another base -- no tables given CRC #20 does give the base change formula on p. 181, but Im guessing this also wouldnt help the original poster since the base change formula is given [1] in virtually every lower level math, physics, and engineering text. [1] Prominently, wherever logarithms are introduced, so it.89s not as if it.89s buried in some obscure place such as a footnote or an exercise that a novice would have trouble noticing. Dave L. Renfro === Subject: Re: computing the logarithm of arbitrary base > hey folks, silly question from someone who prolly never should have embarked > on a 3 year bachelors degree in mathematics... anyway, i would like to > compute the b-base logarithm of a number, but my calculator seems only allow > me the bases e and 10... hints anyone?? > thnks Do you understand how to use logarithms to calculate powers of a number? If you want the b-base logarithm of a number c, you are trying to solve the equation b^x = c So using logarithms (of any base, e.g. e or 10) leads to... === Subject: Re: computing the logarithm of arbitrary base > i would like to compute the b-base logarithm of a number, > but my calculator seems only allow me the bases e and 10 > ... hints anyone?? log(base b)(x) = ln(x)/ln(b) = log(x)/log(b) === Subject: Re: need a ruler? go to my free online/onscreen ruler project > Did you ever need an online ruler while you were sitting in front of > your computer? [NonBreakingSpace]now you can come to this page and use this website to > measure things. > http://home.earthlink.net/~moon8500/davidmoon.html Give them an inch and they think theyre a ruler. === Subject: Re: looking for problems by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKDNse11183; >Hi Todd, >I am not beating the bush around as a you do not express your opinions >in mathematical termslike :you are wrong and here is why. What opinion? In an earlier post I admitted that I didnt know what you were talking about, and thats an honest statement. Several posts later, I still dont know, and wonder why youre taking so long to make your point. Now as far as expressing opinions in mathematical termslike: all youve done except mangle the English language and deliver pompous little sermons is write the Pell equation as x^2 = A*Y^2 + 1. I dont see how I could be wrong about expressing simple bafßement about what youre up to. Nor is there anything wrong about being skeptical. But hey, if youve got a point, youve got a point, and Im happy to listen. Trust me: Im a professional :-) Or, are you >frustated because >you can figured it out? Not particularly. Just cant understand why youre being so coy. >Then say it:I gave up;I am not able do it and enlighten me. OK, I give up. Enlighten me. >Not to imply that is something wrong with me just because you can get >to the end of it.Yes, a,b,c ,Y,x are natural numbers. I implied nothing of the sort. Just make your point already! Todd Trimble === Subject: Re: looking for problems by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKHglN03605; > Hi Todd >I got your point; >Here it is; > Y^2=D*X^2+1 > Case 1: D=2*C-1 > a=Y-X > b=2*X*(C*X-Y) > c=2*X*(C*X-Y)+1 > a^2+b^2=c^2 > Case 2: D=C-1=even number > X must be=2*K > a=Y-X > b=2*X*(C*K-Y) > c=2*X*(C*K-Y)+1 > a^2+b^2=c^2 >Observation:Y and X are INTEGERS:We can invent a new problem,no? >george ghiata I answered your post about X, Y, Z relatively prime, 15 operations, etc etc. I dont know if you were trying to teach me something, or you needed help with something... what exactly are you trying to prove by presenting these vague (and trivial) questions?? Advice: In your response, make an effort to communicate properly in english. Joseph A. === Subject: Re: looking for problems by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKKN7C18432; Hi joseph: Here is in plain english: 1).Given ANY A,B,C relative prime natural numbers find X,Y,Z relative prime natural numbers such that A*X+B*Y=C*Z 2). SOLVE 1) by using only 15(fifteen) ARITHMETICAL OPERATIOnS I think that it is clear now. george ghiata >> Hi Todd >>I got your point; >>Here it is; >> Y^2=D*X^2+1 >> Case 1: D=2*C-1 >> a=Y-X >> b=2*X*(C*X-Y) >> c=2*X*(C*X-Y)+1 >> a^2+b^2=c^2 >> Case 2: D=C-1=even number >> X must be=2*K >> a=Y-X >> b=2*X*(C*K-Y) >> c=2*X*(C*K-Y)+1 >> a^2+b^2=c^2 >>Observation:Y and X are INTEGERS:We can invent a new problem,no? >>george ghiata >I answered your post about X, Y, Z relatively prime, 15 operations, >etc etc. I dont know if you were trying to teach me something, or >you needed help with something... what exactly are you trying to prove >by presenting these vague (and trivial) questions?? Advice: In your >response, make an effort to communicate properly in english. >Joseph A. === Subject: Re: Why do two negatives equal a positive? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKFrbj26194; i have answered this question using the properties of the number line. unfortunately, i cannot post this here since it contains graphics. hence, i have posted it on my webpage at if you have anything to say about it, please mail to abhishek@deydas.com. thank you. >Why do two negatives equal a positive? How is it proven that two negatives >equal a positive when multiplied together? I have always known that a >negative times a negative equals a positive, but it has never made sense to >me. Will someone please make sense of it? === Subject: Re: Why do two negatives equal a positive? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBKDNsc11202; using the field axioms is perfect except for a major ßaw which (atleast in my eyes) has rendered it useless. we are trying to prove here that when a negetive and a positive integer is multiplied the result is positive. why? but in your solution, you have used the same property in the third line without proving it first. >By using the field axioms >(http:// mathworld.wolf ram.com/FieldAxioms.html) >first you can show (-1)(-1) = 1: >(-1)(-1) = (-1)(-1) + 0 > = (-1)(-1) + (-1) + 1 > = (-1)[(-1) + 1] + 1 > = (-1) * 0 + 1 > = 0 + 1 = 1 >and that (-1)a = (-a): >(-1)a = (-1)a + 0 > = (-1)a + a + (-a) > = a[(-1) + 1] + (-a) > = a * 0 + (-a) > = 0 + (-a) = (-a) >So (-a)(-b) = (-1)a * (-1)b > = (-1)(-1)ab > = 1 * ab = ab. === Subject: Re: Is zero even or odd? >>0 cant be divided by itself, > Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1 > It works if the only three numbers in the universe are > 0, 1, and infinity -- A number system that seems very > suited to usenet. Zero is even. You cannot divide by zero. Limits are not division. Infinity is not a number. Computers bugger up the system. --- Shawn === Subject: Re: Is zero even or odd? > 0/0 = 1 > Ah, so 1 = 0/0 = (0+0)/0 = (0/0) + (0/0) = 2 ? Not so fast, if 0/0 = 1 then it follows: 0 + 0 = 2 * 0 1 + 1 = 0/0 + 0/0 = (0 + 0)/0 = 2 * 0/0 = 2 -- Nicholas O. Lindan, Cleveland, Ohio Consulting Engineer: Electronics; Informatics; Photonics. Remove spaces etc. to reply: n o lindan at net com dot com psst.. want to buy an f-stop timer? nolindan.com/da/fstop/ === Subject: Re: Is zero even or odd? posting-account=4l-peA0AAACabaoispHnNpa9VfXI_fbk > I know 0 is neither negative or positive but what about odd/even? I think > its even. It is essentially neutral for it signifies a number that isnt there because it lacks quantity. It is the symbol for nothingness therefore it isnt odd nor even. For example, take the addition of all numbers from -infinity to +infinity, what do you get?...zero!...nothin!....nada! The sum of everything is equal to nothing! In physics, the conservation of energy states that no energy can be created or destroyed. Therefore, if you add up all of the negative potential energy in the universe with the positive kinetic energy, you get NOTHING!....hence the total energy in the universe is zero. Therefore, we are all essentially made up of nothing. Sleep tight! === Subject: Re: Is zero even or odd? posting-account=s1UxvAwAAAAcX9W4GCK8lzXVIWgkSg6e > I know 0 is neither negative or positive but what about odd/even? I think > its even. > Odd numbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7 > Even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8 The majority of the mathematical postulates suggests that 0 is neither positive nor negative; however, that it is an even number. Take into account that Even+Even = Even. Here, 0 can be substituted into any spot as in 6+0=6 to satisfy the postulate. There is also Odd+Even = Odd, and 0 works here too. It can also be put into multiplication postulates such as Even^(any positive integer) = Even. As opposed to Odd^(odd positive integers) = Odd. There are certain undefinable and Ôcircular reasoning postulates. Such as Odd*Even = Even, in which case the quotient is undefined. --------- Steven Xu