Recent content by JanClaesen

No no I think you misunderstood me. The radius is on the y-axis and is, for a circle, a constant, theta is on the x-axis and may take any value. This is a circle, represented in this particular coordinate system by a straight line: y = the radius. In rectangular coordinates the graph is a...

I'm trying to describe the cycloid described by a wheel rolling inside a circle: The (rotor)vector attached to the center of the rolling wheel is described by this equation: r = r cos(w t)e(x') + r sin(w t)e(y') w is the angular velocity of the wheel, e(x') and e(y') are the unit vectors and t...

Okay, but, for example, the arclength of a circle in cartesian coordinates is finite, while the same circle in the polar coordinate system, a straight line (y = the radius) has an infinite arclength, which is too a geometrical property, so appearently not all geometrical properties are...

My question is: for example: the straight line x = y (1.1) or theta = 1/sqrt(2) (1.2) and the circle x² + y² = 1 (2.1) or r = 1 (2.2) In this case 1.1 and 2.1 have the same angle of intersection (so the angle described by the tangents of the straight line and the circle at their point of...

Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?

If a n x n matrix A has an eigenvalue decomposition, so if it has n different eigenvalues, by the way, is it correct that a n x n matrix that doesn't have n different eigenvalues can't be decomposed? Are the more situations in which it can't be decomposed? Why can't I just put the same...

Hello :smile: I don't understand why g(y) isn't the inverse? f: x -> y and g: y -> x I still don't understand why integrating 1/f'(g(y)) doesn't yield me g(y) :smile:

f(x) = cosh^2(x)+sinh(2x) = y f'(x) = sinh(2x)+2cosh(2x) = 3e^(2x) + e^(-x) = y' Let g(y) be the inverse of f(x): g'(y) = 1 / f'(x) = 1 / [3e^(2y) + e^(-2y)] = e^(2y) / [4e^(2y) + 1] Integrating gives: [ 3^(1/2)/3 ]*arctan[ 3^(1/2) * e^(2y) ] + C Now when I plotted this function it...

Yep, thanks again :smile: Is there a human way to do this also for sin(3θ)? Or would that be a computer job? :smile: I'm trying to do this now, but I have a feeling it's quite tough. :smile:

Wow, that was clever, thank you :smile: For those interested: xy = 0.5(x^2+y^2)(x^2+y^2)^(1/2) (where x^2+y^2 = sin^2 (2θ) )

Do you have any hints on how to find the Cartesian equation for r(θ)=sin(2θ), I really can't seem to find it. :)

I'm trying to express the polar rose as an implicit function: r(t)=sin t x = sin t * cos t y = sin^2 t Since sin t * cos t = (1/2) * sin 2t and sin^2 t = (1/2) * (1-cos 2t) (2x)^2 + (1-2y)^2 = 1 4x^2 -4y + 4y^2 = 0 When I plot this, Maple plots a circle, where have I gone wrong?

So how should I approach more difficult math? On a lower math level it is possible to really understand a certain property, relation, formula, ... you can see where it's coming from: intuitive and/or by quickly derivating it in your head. But as the math becomes more difficult, this...

Are electromagnetic waves always caused by a moving charge? A magnetic field can induce current in a conductor if the magnetic flux going through this conductor changes, is this reversible? So does an electric field cause a magnetic field because the electric flux ('through' what?) changes? Is...

Thanks, that was clarifying :smile: Ah indeed, the constant function, the integral value over a certain x-period is relative? So if F(2) - F(1) > F(3) - F(2) 'more' has changed in the interval 1 -> 2, 'what' has changed depends on what the x and y value represent, in the case of distance and...