Robust Posted December 9, 2004 Report Share Posted December 9, 2004 Something that has always befuddled me with regard to contemorary mathematics is how any closed continuum can be described other than by a whole number or ending decimal. If not able to define an exacting relationship between line and arc, how can we ever hope to navigate the stars or determine the resnonant association between particles at the quantum level (any level)? "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Bo Posted December 9, 2004 Report Share Posted December 9, 2004 what do you mean by closed continuum here? Bo Link to comment Share on other sites More sharing options...
Robust Posted December 10, 2004 Author Report Share Posted December 10, 2004 By a closed continuum, Bo, I mean the square, circle, octagon, polygon, etc. "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Bo Posted December 12, 2004 Report Share Posted December 12, 2004 but mathematics describes a lot of things with other things then a "whole number or ending decimal". and i dont think it matters here if the curve is closed, or not. e.g. a circle with coordinates (x,y) and radius R would be described by something like x^2 + y^2 = R^2, where x,y and R are Real numbers. Real numbers are by definition not confined to be a whole number, or ending decimal. Bo Link to comment Share on other sites More sharing options...
Robust Posted December 13, 2004 Author Report Share Posted December 13, 2004 Bo, I think it matters a great deal if the curve is closed or not; if closed, then like the square, a closed continuum. And if a closed continuum, then by neccessity requiring that it's area be defined by either a whole number or ending decimal. There has recently been given a pi value that does achieve that - but best we wait to see how that turns out with the boys upstairs! "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Bo Posted December 13, 2004 Report Share Posted December 13, 2004 can you show me a proof or so that the area is always described by an ending decimal? i don't see any reason why this should be the case... (for example: if we have a square of sides pi, then the area is pi^2, which is not an ending decimal) Bo Tormod 1 Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 13, 2004 Report Share Posted December 13, 2004 yeah, it doesnt make sense to me either... a right triangle with side sqrt(3) and 2 wouldnt come out as decimal area, would it? Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 13, 2004 Report Share Posted December 13, 2004 an area can be seen as the infinite sum of infinitly small dots or lines.... it really doesnt have to be ending decimal... Link to comment Share on other sites More sharing options...
Robust Posted December 14, 2004 Author Report Share Posted December 14, 2004 an area can be seen as the infinite sum of infinitly small dots or lines.... it really doesnt have to be ending decimal... But if the number of dots and/or lines are known and a closed continuum, then why not an ending decimal? In fact, I don't see how it could logically be otherwise. Very confusing to me.... "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
pgrmdave Posted December 14, 2004 Report Share Posted December 14, 2004 The reason for it not being an ending decimal has more to do with our number system than mathematics. Link to comment Share on other sites More sharing options...
Robust Posted December 14, 2004 Author Report Share Posted December 14, 2004 The reason for it not being an ending decimal has more to do with our number system than mathematics. I think you're right....and have to point to the irrational pi as the culprit. It truly is nothing more than an idealistic fabrication of numbers, an abstract logarithm of decimal expansion with no conformity or possibility of end..Time I think it was contested. "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 14, 2004 Report Share Posted December 14, 2004 why does it have to be a perfect ending decimal anyway?and endless decimals is not just irrational numbers,numbers like 1/3, 1/11... are also endless decimals. Link to comment Share on other sites More sharing options...
pgrmdave Posted December 15, 2004 Report Share Posted December 15, 2004 Something that has always befuddled me with regard to contemorary mathematics is how any closed continuum can be described other than by a whole number or ending decimal. If not able to define an exacting relationship between line and arc, how can we ever hope to navigate the stars or determine the resnonant association between particles at the quantum level (any level)? - Pythagoras Perhaps you should have asked why they could be described by numbers other than integers, which would include fractions that cannot be described as decimals. Link to comment Share on other sites More sharing options...
Robust Posted December 16, 2004 Author Report Share Posted December 16, 2004 The reason for it not being an ending decimal has more to do with our number system than mathematics. This is where I run into trouble with maths - terminology - so you'll have to excuse my ignorance. What factors are they? I know of only one example where, say, area of the circle can be described by a whole number using the irrationasl pi (and that by virtue of root 2), giving a value of 1.0 area. The originally known pi value of 256/81 also gives an area by a whole number, but by a diameter at the opposite end of the Base 10 number system and also employing root 2. Something strange going on here that bears investigating. "All things number and harmony." - Pythagoras Link to comment Share on other sites More sharing options...
Robust Posted December 17, 2004 Author Report Share Posted December 17, 2004 Okay, I've been working on it, but still confused as hell as to the concept of unending decimals. Is this to say that the irrational pi - or any pi value forn that matter - is incapable of defining the area to a circle by a whole number? And if it could be so defined, what would that mean? Meanwhile....back to the calculator! Link to comment Share on other sites More sharing options...
pgrmdave Posted December 17, 2004 Report Share Posted December 17, 2004 Why should it need to be an ending decimal, or a whole number? A number is simply a symbol which we use to represent an amount, pi is a symbol we use to represent the ratio of a circle's radius to it's circumference. Link to comment Share on other sites More sharing options...
Tim_Lou Posted December 17, 2004 Report Share Posted December 17, 2004 maybe read a little about the 1!=1 thread?endless numbers can be viewed as infinite sums.... Link to comment Share on other sites More sharing options...
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