>> hows that for inaccurate? LOL a very very small step over the edge of infinitity....... how about over a million times that distance...... oh and we will need a cosmic judge to determine just how far out of position a craft might be..... All space craft must "go" in an orbital path..... just "exactly" what that curve is can not be left to chance (or definition) if you are to get back alive. I know because that is how I got to be stuck on this hunk of rock, LOL
URI: You're still confusing definitions with measurements. Yes. Very well defined, mathematically. Space is curved, but in a way not described by the usual definition of curvature? In that case, you need to specify what new definition you want to use. Otherwise, your statement will be meaningless to anybody else. Pi is defined. Didn't you read my previous post? It has nothing to do with flatlands or any other imaginary land of the pixies. It's a mathematical construct. No. Once you define "flat" mathematically, things either are flat or are not flat. Otherwise, you're using a bad definition and you need to go back to the drawing board to get a workable one. Pi has nothing to do with flatness. You don't run the universe. Yes. It has the value as defined. No. Completely wrong, I'm afraid. Try again. I hope you know better now.
LOL, I am forever apart from this world. Sorry, I just do not agree........ and I should I know, but maybe just maybe there is more to this Yes pi is a definition and in Euclidean geometry (theoretical) pi has a mathematical value. And yes flat, straight and circle and ratio all have precise definitions However the first three of these defined concepts really do not exist in reality. One can draw a circle on a surface that is slightly concave (convex) and its properties will produce a different value for the ratio of diameter to circumference.... a truely 'flat' surface is necessary if pi as defined will yield the value mentioned. Perfect circles do not exist, at the least precession complicates the issue, and at worst eccentricity of orbit just has to be tolerated I use pi, yes your defined pi.... but I live in theoretical Euclidean geometry as an overlay onto space...... but I would be loath to trust my life on predictions drawn from theory to travel space. The theoretical value of pi is a good basis to start, but fudge factors will always be necessary, and even these will change over time. Space navigation is of particular interest to me, so as with most things, there is no last word when dealing with reality. Anyway that is my point of view..... I live in a real world. So I will leave it there... I was just expressing my understanding and my reservations Please Register or Log in to view the hidden image!
URI, Look at it this way if it makes you feel better about it: One definition of Pi is in terms of Euclidean geometry. It's defined as the circumference/diameter ratio you would measure if you could find a perfect circle in perfectly flat space. Suppose you spent a lot of time and care in constructing a real circle, such that it's circumference/ratio diameter should be, say, within 0.01% of π. If you then accurately measured the circumference/diameter ratio and got 3.000 instead of 3.142, you could use that as evidence that the space your circle was in was curved. Also, π comes up in other places - not just in Euclidean geometry. The values of x for which sin(x) = 0 are all multiples of π, for example. Or if you feel like tossing coin experiments, it can be shown that the probability of throwing equal numbers of heads and tails tends to 1/sqrt(n&piPlease Register or Log in to view the hidden image! for 2n coin tosses, as n --> ∞. All these π's are one and the same.
>> The values of x for which sin(x) = 0 are all multiples of pi ah Ha That is the situation in spin grav's planetary positions in the Solar System A sine wave extending from the centre, the Sun.... to the planets where each planet sits on an integer node..... N/pi^2n series Thank you for your sharing of knowledge przyk
>> The values of x for which sin(x) = 0 are all multiples of pi >>> ah Ha That is the situation in spin grav's planetary positions in the Solar System A sine wave extending from the centre, the Sun.... to the planets where each planet sits on an integer node..... N/pi^2n series A minimum energy series Thank you for your sharing of knowledge przyk
How about Pi(x)? No one talked about that. haha. But URI, I still do not get why you are dissatisfied with the value of pi. You think pi useless because you cannot find it in reality with perfect precision?
>> I still do not get why you are dissatisfied with the value of pi. LOL not dissatisfied with the concept of pi only have objections to the "inferred" nature of this theoretical mathematical construct Pi is supposed to be 'transendental'..... meaning it has no repeating decimal part.... theoretically YES, but... On Earth we can dream..... just for me dreams are not reality. I use pi (the symbol) to overlay Euclidean geometry onto the Solar System and even use its standard numerical value in some calculations..... however I remain aware that I am out of line, and pi should forever remain just a concept that IMO will yield different mathematical values in different places in this Universe. Here on Earth, we have control, we have stablility, but we are so small on a cosmological scale In space we don't even know what "size" is, so I remain humble, and accept that some variables can not be universally determined and only local variable can be known. so not adverse to 'values', just aware that they may not be universal.
No, 'transendental' means it is an irrational number that cannot be the zero of a finite polynomial with integer coefficients. We use pi to approximate how the universe works and what it will do. I think it is good enough. If you do not want to use Pi, feel free to derive your own equations that work equally well. I think most would rather deal with C = Pi*2*r instead of some complicated equation that takes into account variable curvature and makes no reference to pi.
pi is the Famous Transcendental number forget about meditation and enlightenment pi transcends all numbers.... it has no end... a mathematical definition.
We did not define Pi to be transcendental... it's a consequence of definitions and axioms. We can see Sqrt(2) is the positve root of x<sup>2</sup> - 2 = 0, but try to find a polynomial with rational coefficients that has Pi as a root.
OK lets us define pi IMO It is the ratio between the 'line' (straight) and the curve (arc, standard circular) I suspect the basic geometric consideration is the diameter and the semi circle length D = pi*R........... (1) I have never suceeded to generate all the relations between circular to spherical rotations ie follows from (1) the length circumference = 2 X pi*R....... (2) and the area modified (lenght RXR) or Area circle = pi R^2......... (3) rotate that and ? ie multiply by pi ___> volume of sphere pi*R^3 but the classic 4/3 comes in.... how? In simple curved figures there can only be one pi, one ratio to change length, because the curve is all the same In more complex figures pi^2 may come into the formula It would be instructive to derive all the formula from logic.... rather than rote
in what part of the universe will pi not be equal to what it is here on earth? a circle is a circle no matter where it is. if you draw a circle on a piece of rubber and stretch it even slightly it is no longer a circle.
>> in what part of the universe will pi not be equal to what it is here on earth? well its not equal to the theoretical value even on Earth pi is very much dependant upon 3 things, flatness, straightness and 'circularity' the more the circle centre is 'out-of-plane' with the circumference the smaller pi becomes Theoretical pi is a maximum.
this doesn't answer my question but now that you mentioned it pi is not theoretical pi is exact. it is the number 3.14159265. . . that is an approximation circumference/diameter equals pi. pi approximatly equals 3.14159265
I don't see the necessity of even discussing pi as a variable. Pi refers to circles....perfect circles, and in pure math the term perfect circle should be redundant anyways. If you apply math to reality, you make the assumption that the axioms of whatever math youre using are consistent with reality itself. Does it only strike me as strange that something as "perfect" as a circle or sphere could embody a ratio that can never be exactly known? A ratio with decimal points that not only never end, but are almost by definition......random? There always seemed to be something faintly amiss, or even contradictory about that........
At least leopold and alyosha get it. It seems URI wants numbers to refer to reality. If that is true, stay away from anything that doesn't have to do with applied mathematics. You are never going to get mathematics to explain reality 100%. And I still do not get what the "theoretical value of Pi" means. Pi is a definition. If you want a different definition, you need to refer to something other than Pi. Measure the circumfrence of Earth at the equator if you want and derive a constant from it. I am fine with that, but please do not question a DEFINITION in mathematics.
