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You are not logged in. #26 20130108 07:42:52
Re: The Structural Analysis  mathematics of the futureOn this question: "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #27 20130108 08:13:17
Re: The Structural Analysis  mathematics of the futureI will try again. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #28 20130108 09:11:24
Re: The Structural Analysis  mathematics of the future"number of slices" Bob Try to translate by means of the dictionary start top from Russian. I here all accurately wrote all. I feel that my robot doesn't translate all sense of that that I want to inform you. http://bolshoyforum.org/forum/index.php?topic=297286.0 I will try to explain a bean to you so. Present that on the plane there is circumference of any radius. ANY (! ! ! ) It is the line, it  not the area (! ! ! ) Now you to it add one more circumference in the same plane. Either it is more or has no value but such that between these two circumferences it was impossible to insert one more less. It already area, instead of line. Elementary Square, the most smaller also is differential of the area of a circle. Any more line. But already area! It also is:  means two points (1=dx/dx, 1=dr/dr, 1=dl/dl) nearby and distance between them. It is one point increased by distance between them  an elementary piece: The sum of elementary segments of line (pieces) lying in one direction (not in parallel):  is a line. One point  One point it yet length not segment of line. Three points  not elementary. Integration is an absolute measure it doesn't depend on a unit of measure which the person can choose randomly. You understand this? P.S. I try to translate twice: from Russian into English then from English into Russian  sense is not adequate. I don't know what to do. Last edited by 21122012 (20130108 14:11:57) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #29 20130108 19:01:52
Re: The Structural Analysis  mathematics of the future<structural analysis> is true => <cone test is good>
I agree. Translation is one word at a time. Phrases are not translated properly. If a word has two meanings, translation may pick the wrong one. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #30 20130108 19:50:56
Re: The Structural Analysis  mathematics of the futureGive me the test. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #31 20130108 20:06:39
Re: The Structural Analysis  mathematics of the future
Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #32 20130109 06:05:23
Re: The Structural Analysis  mathematics of the future
Didn't understand. You look post #28 the most top line. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #33 20130110 06:49:18
Re: The Structural Analysis  mathematics of the futureI have made a new spreadsheet. eg. The G column formula is =1/3*PI()*G4^2*G5 Row 7 calculates values of pi r^2. The formula for the G column is =PI()*G4^2 Row 9 calculates the area of a rectangle below the curve. This is the yellow area shown in my second diagram. The formula in the G column is =G7*(H4G4) Row 10 sums these values. Formula in the G column is =SUM($B$9:G9) Row 11 calculates the area of a rectangle above the curve. This is the sum of the yellow and green areas in my diagram. The formula in the G column is =H7*(H4G4) Row 12 sums these values. Formula in the G column is =SUM($B$11:G11) Row 10 gives the lower bound for the area under the curve. 44861 Row 12 gives the upper bound for the area under the curve. 53005 Therefore 44861 < area under curve < 53005 The correct volume of the cone is 20579 Conclusion: the following formula is NOT correct. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #34 20130110 09:47:28
Re: The Structural Analysis  mathematics of the futureBob! . If you put just the same circle, the circle area increased by distance to other circle not including other circle is will be elementary volume of . Because Though eventually will reach only size Because Now most important! When you build cone volume with height equal to basis (!) radius that at distance from a beginning point (from top) at any distance on height with you will be placed the circle with the same radius (!) is a key to understanding of integration! In any point of height there will be element of Planimetrics in the form of a circle of the same radius. If height isn't equal to radius, and is its function, at each distance from top there will be a circle CORRESPONDING to value of function! Therefore no trapezes will exist! Trapezes are delusions (errors) of Calculus. They have no place to undertake. They won't appear anywhere because there will be no two distances from top on which there will be identical circles! There will be only elementary truncated cones. In what difference between and Which in the first case creates volume a cone, and in the second case creates cylinder volume???!!! Everything is concluded in a difference of these two expressions: prompts that at distance from top circle will settle down. prompts that at any distance from top IDENTICAL circles: will settle down. You understand? P.S. In everything the limit which uses Calculus is guilty. Because this limit it is possible to give only presentation of VALUE of the DERIVATIVE but not the most derivative. In Structural Analysis the absolute limit on accuracy for receiving derivative function instead of its value is used: Last edited by 21122012 (20130110 13:47:49) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #35 20130111 06:51:02
Re: The Structural Analysis  mathematics of the futureI do not understand why you use calculus at all in your structural analysis. fails to give you the correct result. Of course you get the volume of a cylinder if you treat pi r squared as a constant. Most mathematicians know you have to change the 'r' term to a function of 'h' before you integrate. I see no point in continuing until you clear up what you are trying to do in post 22. Now I look at post 22 again I see that your integration for a cylinder is wrong too. Please use the upper bound / lower bound method to justify these or change them. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #36 20130111 12:56:35
Re: The Structural Analysis  mathematics of the futureI translate from English. I can't understand that you want. What mine have to be actions? "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #37 20130112 03:20:12
Re: The Structural Analysis  mathematics of the futurehi 21122012 How can this be from o to r ? The variable is h. Note: And you say Note: This is my last word on integration. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #38 20130112 06:05:07
Re: The Structural Analysis  mathematics of the future
That is not correct. You cannot have h both in the integration limits and as the variable which you are integrating with respect to... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #39 20130112 06:18:02
Re: The Structural Analysis  mathematics of the futureHi anonimnystefy;
Of course you can. 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. #40 20130112 06:20:53
Re: The Structural Analysis  mathematics of the futureThen you could have something like The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #41 20130112 06:29:51
Re: The Structural Analysis  mathematics of the futureHi; 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. #42 20130112 06:40:40
Re: The Structural Analysis  mathematics of the futureAlpha understand it differently then they should be understood. It looks at the two k's (and x's) as different, while they are in fact the same k (x)... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #43 20130112 06:43:55
Re: The Structural Analysis  mathematics of the futureNo, they are not the same, in the integral you do not substitute for the x in the dx. The index of summation obviously is the same. 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. #44 20130112 06:46:14
Re: The Structural Analysis  mathematics of the futureHi bobbym The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #45 20130112 06:49:57
Re: The Structural Analysis  mathematics of the futureOne thing at a time. is not allowed. 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. #46 20130112 06:58:08
Re: The Structural Analysis  mathematics of the future
Hi bob! It is a special case of a general view:
It is a special case. You choose only one option from all possible options of height. Such, when height равнв to basis radius. I didn't think that it is difficult for understanding.
I couldn't say such nonsense. It not cone volume, because it cylinder volume.
You don't understand difference of a variable from value of a variable which is constants. variables, then made their dependent Then took values of these dependent variables these values can't become independent variables It is absurdity! Function of a type: in a geometrical form of a mnterpretation where  x radius, y  height can be constructed only in the form of cylinder volume. The volume of cone can be constructed only if Excuse don't take offense at me but with such representation of integration as at you it is impossible to accuse me of mistakes. It is frivolous. If you saw it as someone somewhere goes figures in chess you will speak to the grand master that you will win against him in advance. Once again I am sorry but you told the first that I am mistaken. I am not mistaken. I can teach as to do correctly those who is mistaken. Last edited by 21122012 (20130112 12:08:41) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #47 20130112 07:06:11
Re: The Structural Analysis  mathematics of the future
This isn't an error. It is an unnecessary duplicator of a variable of a mntegrirovaniye. In the main theorem of calculation it is a case when the variable doesn't lie in an interval and is the interval end. Last edited by 21122012 (20130112 16:56:29) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #48 20130112 19:34:25
Re: The Structural Analysis  mathematics of the futurehi 21122012,
There are many formulas with three variables which will allow you to choose two variables 'independently'. The three are still related. You may choose D = 24 Km, and S = 4 Km/hr. This was a free and independent choice for D and S. But they are still related by the formula. example 2 is the equation for a circle, centred on (0,0) You may choose any values for x and y because any point will lie on some circle. But x and y are related. example 3 Once again you may choose u and t independently but the formula still holds. Why are you so reluctant to accept that, for a cone, there is a formula connecting r and h? If r is fixed, then it is not a cone is it? r has to vary as h varies to make a cone. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #49 20130113 07:09:11
Re: The Structural Analysis  mathematics of the futureHy bob We integrate this derivative and we receive... cylinder volume: ...." You remembered why we started talking about a cone and the cylinder? Therefore when we tell about volumes of these two geometrical figures that I always I speak about them and I remember the reason for which we speak about it. And you tell everything that doesn't treat at all a subject of our dispute. You didn't prove to me that a formula it is cone volume. And still didn't give integral for calculation of volume of the cylinder which would differ from this formula THOUGH SOMETHING! Last edited by 21122012 (20130113 07:10:17) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #50 20130113 09:07:37
Re: The Structural Analysis  mathematics of the future
Yes I did. But it is so clear in my head I will do it again. Obviously h = r = 0 gives C = 0 So The reason you get the formula for a cylinder is because you insist on saying pi r^2 is constant. Of course it isn't for a cone, but it is for a cylinder. Note: This work has nothing to do with partial derivatives. As r and h are related it is possible to avoid any parrtial derivatives at all simply be using the relationship between r and h. If you will not accept this, then we might as well cease communicating. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 