Nootropic Posted October 23, 2008 Report Posted October 23, 2008 Annoying is more like an understatement. I would suggest everyone throw in the towel on this one because trying to convince him was probably like trying to convince the King of Spain the Earth wasn't flat. Obviously we are right. Let him ponder in his own little world filled with badly constructed "scientific" experiments and wholly incorrect conclusions. Anybody in the mathematics community would immediately dismiss such a severely flawed argument--and I suggest we do the same. Quote
CraigD Posted October 23, 2008 Report Posted October 23, 2008 Guadalupe, what you are claiming appears to be this:All definitions of the [math]\pi[/math] that use arithmetic, such as Liebniz’s formula [math]\pi = \sum_{n=0}^\infty \, \frac{4(-1)^n}{2n+1}[/math], or Liu Hu’s algorithm, are wrong, because the number they define is a “false value”.Physically building circular objects, such as thin deposits of graphite or ink on fibrous mats (ie: pencil or pen on paper) or cylinders (eg: lathe-turned wood or metal pieces) and measuring them their diameters [math]D[/math] and the circumferences [math]C[/math] and dividing these 2 values ([math]\pi = \frac{D}{C}[/math] is correct, the resulting number being a “true value”.What you appear to mean by “true” and “false” are the more recognized math terms “rational” and “irrational”. A rational number [math]q[/math] is one that can be written as an integer divided by an integer ([math]q = \frac{a}{b} : a,\,b \in \mathbb{Z};\, b \not=0[/math]). An irrational number cannot be written this way. You’re receiving a bit of polite ridicule at hypography, I think, because nearly all of the regular readers of the Math forum have reasonably good understandings of the idea of rational and irrational numbers, but you show no sign of being. Rather, you seem to believe that irrational numbers are fundamentally wrong. You’re far from the only person to have ever thought this. I, and I suspect most people who have studied math have, at some time in their intellectual development, suspected that, if you could somehow just pick the right 2 integers – perhaps very large ones, but still integers - constants like [math]\sqrt{2}[/math] and [math]\pi[/math] could be written as simple fractions. Eventually we were introduced to proofs or irrationality such as these (or, if we were really sharp students, derived ones ourselves), and came to reject this “if you could just somehow pick” sentiment. I hope you can, too, Guadalupe, because the concepts you appear to not understand or actively reject are beautiful and pleasing. Quote
Qfwfq Posted October 23, 2008 Report Posted October 23, 2008 A polygon is composed of a finite/infinite set of straight line segments, and a circle is not. A circle by definition is a smooth plane closed curve whose points are all on the same plane and at the same distance from a fixed point (the center). A polygon is by definition a closed figure with straight line segments and a regular polygon is a polygon that has equal sides and congruent angles.Thanks for the lesson but I wasn't disregarding such things. Guadalupe I asked you if you have studied the basics of topology and metric spaces, apparently you have not. Get back to us here when you understand topological notions such as Cauchy sequences and completion. I think he's trolling and it's getting annoying!And perhaps you are even correct Jimoin! Quote
Guadalupe Posted November 8, 2008 Author Report Posted November 8, 2008 What, EXACTLY, were the measurements of the circumferences of those circles? Hi! C1ay :hyper: Going low tech, I used a lead pencil for drawing a perfect circle instead of ink as to avoid compromising the smooth and unblemished surface. Below are two examples: Working with a 20 inch diameter, I carefully drew and measured the circumference of a perfect circle, it measured exactly 63 inches. I divided the 63 inch circumference by the 20 inch diameter and came to exactly 3.15 as Pi. This was great news. Now, working with a 30 inch diameter I carefully drew and measured the circumference of a perfect circle, it measured exactly 94.5 inches. I divided the 94.5 inch circumference by the 30 inch diameter and it came to exactly 3.15 as Pi. This confirmed my findings, that 3.15 is Pi, thus remaining constant and finite. Eureka! This process of drawing and measuring the circumference of a perfect circle was less expensive and low tech, LOL!!! But there may be other means of proving that 3.15 equals to Pi. :) Quote
C1ay Posted November 8, 2008 Report Posted November 8, 2008 It sounds kind of like you need to practice your measuring methods a bit... Quote
Zythryn Posted November 8, 2008 Report Posted November 8, 2008 OK, great start.Now, how did you measure the circumference?Then, did you measure the outside of the pencil mark, the inside, or the middle?Also, how did you draw the circle? Free hand, using a string tied to a pin a the center, using fishing line tied to a pin at the center, etc?Next, how many measurements did you make of each size? Quote
Guadalupe Posted November 8, 2008 Author Report Posted November 8, 2008 Hi! CraigD :) Guadalupe, what you are claiming appears to be this:[*]All definitions of the [math]\pi[/math] that use arithmetic, such as Liebniz’s formula [math]\pi = \sum_{n=0}^\infty \, \frac{4(-1)^n}{2n+1}[/math], or Liu Hu’s algorithm, are wrong, because the number they define is a “false value”. By use a false value to represent Pi and using it in any equation such as Liebniz’s formula will always give an accurate approximation of a correct answer. Physically building circular objects, such as thin deposits of graphite or ink on fibrous mats (ie: pencil or pen on paper) or cylinders (eg: lathe-turned wood or metal pieces) and measuring them their diameters [math]D[/math] and the circumferences [math]C[/math] and dividing these 2 values ([math]\pi = \frac{D}{C}[/math] is correct, the resulting number being a “true value”. We asked ourselves, “Is a circle a polygon”? The answer was no because, a polygon is composed of infinite set of straight line segments and a circle is not. We can make an infinite amount of polygon/regular polygon that is as close to a circle as we want, the more sides we give it, the more it will appear to look like a circle. A circle by definition is a smooth plane closed curve whose points are all on the same plane and at the same distance from a fixed point (the center). A polygon is by definition a closed figure with straight line segments and a regular polygon is a polygon that has equal sides and congruent angles. This method of a polygon with infinite number of sides will always give us an accurate approximation of a false value for Pi. My guess would be that for over four thousand years, this method of a polygon with infinite number of sides has always been the “norm” in finding the value of Pi and no one has stop to question it. :cup: Quote
Essay Posted November 8, 2008 Report Posted November 8, 2008 OK, great start.Now, how did you measure the circumference?Then, did you measure the outside of the pencil mark, the inside, or the middle?Also, how did you draw the circle? Free hand, using a string tied to a pin a the center, using fishing line tied to a pin at the center, etc?Next, how many measurements did you make of each size? Yes, I tried a low-tech method too. Obviously the accuracy of anything after tenths is going to be a bit suspect, IMHO. [measurements on a sheet of printer paper in cm.]27.9/9 = 3.1 27.92/9 = 3.10222222222222 27.92/ 8.95 = 3.1195530726256983240223463687151 27.9/ 8.9 = 3.1348314606741573033707865168539 27.92/ 8.9 = 3.1370786516853932584269662921348 27.92/ 8.88 = 3.1441441441441441441441441441441 Well, I just made up that last 8.88 measurement to see what range I needed to be around. I took a sheet of notebook paper and measured it in millimeters. Eleven inches came out to be about 27.9mm, or maybe a bit more (27.92). Measuring the diameter was quite difficult, but I just kept adjusting the string on top of the slightly oblong shape created when I taped the long ends together. Eventually I got a shape that gave me the "same" measurement when I measured at right angles (rt./left vs. up/down). Now this was done free hand (not on a stable surface, so it can't be very precise), but it was a lot of trials so it's fairly accurate. If I "make up" 27.93, and use the 8.9 number which I think may be a bit low anyway, then we get:3.1382022471910112359550561797753. Well, maybe 8.9 isn't too low; maybe it should be 8.89:27.93/8.89 = 3.1417322834645669291338582677165.Well finally that's pretty close, but with lots of creative measurements, eh?=== Now even if I shoot for the other end of the error bars and go with 9.1mm for the diameter, and 27.85 circum.,we get at least: 3.06043956043956043956042956043956, or at most,(27.93/ 8.8) would be 3.1738636363636363636363636363636. Those average out to 3.1171515984015984015984015983998 What odd patterns in those long decimals.... But this is all pretty close to the 3.1415....=== Let's see: 11x 2.54 = 27.94 cm.Why didn't I do that first: :)27.94/ 8.9 = 3.139...so the diameter must really be slightly lower: about 8.893....27.94/8.893 = 3.14179 And see, this is generating unwarranted, unfounded "accuracy" of hundredths and thousandths.... Any test should be repeated on different sized circles too (which should show variation in accuracy). ~ :hyper: Quote
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