05 Apr '07 19:48>
Originally posted by FabianFnasso there is definately a chance! "dumb and dumber"😵
Is as possible as you and me reaching the speed of light.
Originally posted by treborbassettWell, we are now discussing the definition of words.
Pi is defined as the ratio of the circumference of a circle to its diameter in Euclidean geometry. It is a constant. Its value does not change, irrespectively of what geometry is being investigated, in the same way that 4 or root 2 don't change values.
What you mean is that in certain structures the ratio of circle's circumference to its diameter ...[text shortened]... circle's circumference to its diameter in Euclidean geometry, and therefore not equal to pi.
Originally posted by FabianFnasYou're quite right: we are discussing the definition of words. In particular, we're discussing the definition of the word 'pi'. But I'm afraid your definition is quite simply wrong (in the sense that it disagrees with what mathematicians mean by 'pi'😉. It is not defined as the function that accepts a circle (and perhaps a geometry, both suitably defined) as input and yields as output the real number that is the ratio of that circle's circumference to its diameter. 'Pi' simply refers to a number, in the same way that '1' and '2' do. The number to which it refers does not change.
Well, we are now discussing the definition of words.
Originally posted by FabianFnasWhat you are saying doesn't work. Think about the area enclosed by a circle on a 2-sphere. The distance from the pole is theta and the area element is Sin(theta) (Assume the sphere has unit radius). When you work out the area enclosed by the circle it comes to 2 pi (1 - cos(theta)). If theta is small then Cos(theta) = 1 - theta^2/2 + ignored terms. So we get the area of the enclosed (small) area as pi theta^2, as we'd expect having taken the Euclidean limit. circumference = 2*pi*sin(theta) which again gives us 2 pi theta in the limit that theta is small. In non Euclidean geometries the circumference of a circle is not as simple a function of radius (in this case theta) as in Euclidean geometries, you'd need a different value of pi for each circle radius and it loses it's general meaning. pi is ratio of a circles circumference to it's diameter - in the limit that the diameter is zero in all geometries.
Well, we are now discussing the definition of words.
If pi is defined 3.14... in Euclidian geometry, then what is it defined in non-Euclidian geometry? I would say that the value of pi defines how non-Euclidian the space really is. When pi is 3.14... the geometry is flat, as Euclidian space should be.
In Euclidian geometry, of course pi is a constan ...[text shortened]... it hyperbolic? The answer is at hand. Or not. We have no methods to measure circles this large.
Originally posted by bloodyboyTo get back on topic;
If you are traveling at the speed of light would you be invisble? because the light could not catch up to you casue you would be going faster. but then would you be visible from the direction that you are moving becasue you would run into the light rays which would then reflect off of you.???
Originally posted by FabianFnasI was quoting an american movie, dumb and dumber when the main character asks what his chances are of dating this beautiful woman. She replies one in a billion, and he says so you mean there is a chance!
Oh, you think it is actually possible to reach light speed? Not only near that speed?
Well, I don't.
Originally posted by joe shmoActually it was 'one in ten million'. OH, so I HAVE A CHANCE. she gives him a funny look, one of the best scenes in the movie.
I was quoting an american movie, dumb and dumber when the main character asks what his chances are of dating this beautiful woman. She replies one in a billion, and he says so you mean there is a chance!
Originally posted by joe shmoAh, I didn't know that reference, but now when you say it, a remember that line vaguely. 😀
I was quoting an american movie, dumb and dumber when the main character asks what his chances are of dating this beautiful woman. She replies one in a billion, and he says so you mean there is a chance!
Originally posted by treborbassettWhen I was a boy they told me that you can't take the square root of a negative number. I took that as a truth. Later they told me that in R it is impossible, but in C it is and they gave me a wonderful new toy to play with.
But I'm afraid your definition is quite simply wrong (in the sense that it disagrees with what mathematicians mean by 'pi'😉.
Originally posted by FabianFnasIn any geometry the ratio of the circumference to the diameter of a circle is pi in the limit that the radius is zero. Non-Euclidean geometries are locally flat so you can recover the c = pi d rule as a limiting case. In non Euclidean geometries the ratio of the circumference of a circle to it's diameter is not a constant so trying to define pi as a simple ratio doesn't work unless you take the limit that the diameter goes to zero when you get the same answer as in Euclidean space.
When I was a boy they told me that you can't take the square root of a negative number. I took that as a truth. Later they told me that in R it is impossible, but in C it is and they gave me a wonderful new toy to play with.
Newton told us the wonders of physics and everyone thought that all makes sense. Then came Einstein that said, yes in ordinary l ...[text shortened]... tence (as Galileo (?) did: "but still she moves" ) with "but only in Euclidian geometry".