Robust Posted December 18, 2004 Author Report Share Posted December 18, 2004 maybe read a little about the 1!=1 thread?endless numbers can be viewed as infinite sums.... I did read that thread, of course. Why then, I have to ask, isn't the closed continuum of the square or polygon then described by infinite sums? Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 18, 2004 Report Share Posted December 18, 2004 it can.....just like the integral stuffs in calculas.any area can be cut into tiny rectangulars, the sum of the these rectangulars would be a approximiation of the total area....as the "closed continuum" is divided in smaller and smaller rectangulars and to infinitely small rectangulars, the estimated area would be approaching the actual area of that continuum.... Link to comment Share on other sites More sharing options...
Bo Posted December 19, 2004 Report Share Posted December 19, 2004 it is just a convention that 1 with an infinite amount of zeroes behind it is just called 1, and not 1,0000...000 Bo Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 19, 2004 Report Share Posted December 19, 2004 hehe, i didnt think of that..yeah, in scientific measurment, no one is sure if something is exactly 1 or 2, or 1/3.i mean nothing has infinite amount of significate figures... according to uncertainty principle. hmm, it seems to me that rational number doesnt exist in the nature..... since nothing is exact ending decimal.. Link to comment Share on other sites More sharing options...
pgrmdave Posted December 20, 2004 Report Share Posted December 20, 2004 hmm, it seems to me that rational number doesnt exist in the nature..... since nothing is exact ending decimal.. Rational numbers do exist in nature, but not in theory. One can be sure that there are 638 members of this forum, but that number, in theory, is not exact, while the amount in reality is. Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 20, 2004 Report Share Posted December 20, 2004 yes, your right..since photons are quantized by h.....yes, rational numbers do exist... :D Link to comment Share on other sites More sharing options...
Robust Posted December 23, 2004 Author Report Share Posted December 23, 2004 yes, your right..since photons are quantized by h.....yes, rational numbers do exist... :D But what about the irrational numbers like Euler's irrational pi? Is it possible for the irrational pi to describe the area d the closed continuum by a whole number? And if not, why not? Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 23, 2004 Report Share Posted December 23, 2004 yes, pi is defined as the ratio of circumference of a circle to its diameter, it is a artifical number made to related these 2 quanities. calculations were made to relate the radius to its area based on the definition of pi....and many further applications of pi were discovered. Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 23, 2004 Report Share Posted December 23, 2004 to prove area=pi r^2:imagine a circle being cut into different size of circle (not filled) from the orgin.....1st one would be a dot at the orgin, the last one would be the circumference of that circle...there are infinite amount of these circles being cut, since they are infinitely thin.the area would be the sum of all thses different circumferences: pi d1 + pi d2 + pi d3.... pi d,factor pi out, get pi (d1 +d2 + d3 + d4 ..... + d), whats the sum of these ds then?imagine these "lines" being put on top of each other, with the the longest on the base, and the shortest (the dot) at the top. therefore forming a triangle, it goes from 0 to d, with a height of d/2, since it changes in both ends (diameter decreses from both side of the circles), so, the height is not d but d/2...therefore the area would be: pi (base * height /2 ) = pi (d* (d/2) /2) , since d/2 = r, rewrite the equation, get area= pi r^2.well... this is something pops out in my head... dont know if it makes sense to you. Link to comment Share on other sites More sharing options...
Robust Posted December 24, 2004 Author Report Share Posted December 24, 2004 yes, pi is defined as the ratio of circumference of a circle to its diameter, it is a artifical number made to related these 2 quanities. calculations were made to relate the radius to its area based on the definition of pi....and many further applications of pi were discovered. Then please give an example where pi defines the area of a circle by a whole number - or for that matter, by even an ending decimal. I just know it has to be by reason of the circle being a closed continuum. "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
pgrmdave Posted December 24, 2004 Report Share Posted December 24, 2004 How about a circle with a radius of 1/(sqrt pi) ? the area would be 1. Link to comment Share on other sites More sharing options...
Robust Posted December 24, 2004 Author Report Share Posted December 24, 2004 How about a circle with a radius of 1/(sqrt pi) ? the area would be 1. Exactly....and the formula holds true for any pi value given. So, returning to the squared circle thread for the moment, if the standard quadrature formula is capable of describing area of the circle by a whole number, should it not also be capable of squaring the circle?In this instance anyway, how could either be anything but 1? "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 24, 2004 Report Share Posted December 24, 2004 what are you trying to prove here?what do you mean by squaring the circle?... how is it meaningful in any way?please provide some clarification. maybe i'll spend some time on the squaring circle thread.. anyway... the radius of 1/(sqrt pi) is a theoretical number, it is made artifically so that the area of the circle is 1. it is never possible to have such length in real life. Yes, squaring the area would give you same value--one, but what is it for?assuem the area of a circle is 1 m^2, squaring it would give you 1m^4?!! how is it meaningful as a unit? do you mean a 4 dimensional object or?... area^2 and area are not the same thing, even if their values are the same..... the concepts and units are totally different. Link to comment Share on other sites More sharing options...
Robust Posted December 25, 2004 Author Report Share Posted December 25, 2004 what are you trying to prove here?what do you mean by squaring the circle?... how is it meaningful in any way?please provide some clarification. maybe i'll spend some time on the squaring circle thread.. anyway... the radius of 1/(sqrt pi) is a theoretical number, it is made artifically so that the area of the circle is 1. it is never possible to have such length in real life. Yes, squaring the area would give you same value--one, but what is it for?assuem the area of a circle is 1 m^2, squaring it would give you 1m^4?!! how is it meaningful as a unit? do you mean a 4 dimensional object or?... area^2 and area are not the same thing, even if their values are the same..... the concepts and units are totally different. I don't see how you can say that 1/sqrt(pi) is a theoretical number. All numbers are real in that they associate one dimensional state with another. What else do we have? I think squaring the circle is an imortant consideration, particularly in view of latest astronomy questions considering the possibility of a flat universe, at leastn in a configurative sense. If by the quadrature formula you superinscribe the circle with the square, one finds that both the lines intersecting the arc and those extended beyond are all directly defined by pi - interesting stuff - to me anyway. Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 25, 2004 Report Share Posted December 25, 2004 the problem is that pi itself is an irrational number, it can be described as infinite series.in real life, no matter how precise one draws a line, it is impossible to have an endless decimal.since a measurement cannot have infinite significate figures, while pi has infinite decimal. therefore, after one's measurement reach a certain decimal, it would be impossilbe to tell what the next decimal is in that measurement. Link to comment Share on other sites More sharing options...
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