I've never done it but there is also the marshmallow microwave experiment, your supposed to see the wavelength as bumps in the surface. What does that represent?
http://www.physics.umd.edu/icpe/newsletters/n34/marshmal.htm
Using the program to get the graphs there i put in the forumla for L(θ) and it has an option to integrate for area and it gave me 2.23...so my question is why can't I integrate for area this way? the distance from the point to the region being measured makes it impossible to use theta to integrate?
So here is a graph on a unit circle centered at origin, y=sqrt(1-x^2) and a line that passes through (d,0), d=1.5, the slope of that line is -tan(arcsin(r/d))=-tan(arcsin(1/1.5)), as you can see it is the correct slope, so greater than that there are no points of intersection, and less than that...
out of interests...d>r, (d,0) is a point outside the circle. So arcsin(r/d) should I think somehow be the angle, relative to the x-axis, that a tangent line to the circle passes through (d,0)
Does the root not go away from the fact that I am using L(θ) as r in .5r^2θ so .5(L(θ))^2θ and the...
I put it all together to get:
A = \int_{-\arcsin(\frac{r}{d})}^{\arcsin(\frac{r}{d})}{\frac{1}{2}(4r^2-4d^2\sin^2(\theta))}d\theta = 2r^2\theta + d^2\sin(2\theta)-2d^2\theta |_{-\arcsin(\frac{r}{d})}^{\arcsin(\frac{r}{d})}
A = 2\sin^{-1}(\frac{1}{1.5}) +...
Say we have a circle of unit radius centered on the origin, and another point on the x-axis d units away, were we to draw a line at angle θ relative to the x axis, cutting across the circle at either 2, 1 or 0 points, the length of the chord made(or not made) is
L(\theta) =...
Things also appear dimmer from further because the waves are more 'spread out', imagine a sphere with lines coming straight from the center, the further out you get, the more distance between those lines.
Also, if you consider an empty universe with a line going through it and it's just me and that line, then yeah, you are correct, it just rotates I guess, but if you have some arbitrary point of reference then you can know you are either + or - that point, and come up with a convention, just as...
I don't know anything about mono/di -poles, but since the north and south poles are opposite, and the field lines I believe are said to originate at one and terminate at the other, I would think that there is only one of those rules, causing loops to "move" through the center in an oriented...
So can you better define "translational freedom"? Say we take the plane the line is into be the x,y plane, and let's say the line is x=1; A vertical line going through '1,0', So what I think your saying is that we can add or subtract Δy to all the points and it leaves the same line right? I...
Very interesting result... So that is also the most general equation for this sort of thing? As that can be used as n=128th notes or 256th notes, then just you number of n per beat goes up, but for instance n=12 would work for 1 measure of 6/8 going to 16ths? 2 beats, 6 divisions per beat.