Yeah, its the cool 3d stuff that makes calculus come alive.
Once you "get" what a double or triple integral is "doing", its just... really cool. I dunno why. I think because you get this kind of kinesthetic feel for this infinite sum of infinitesmal slivers of this abstract shape... makes my brain happy.
Or when you do integrals in polar co-ordinates, and you realise the integral is adding up these tiny elements of surface area, rotated around a point on the axis, and then that happening for every point on the axis and being summed along the shape... haha. It's like a weird brain massage.
It's that marrying of the hard analytical solution with the "aha!" of visualising the dynamics and the geometry. Something about that is cool.
Then again, I think lots of things can give you that same "aha!" kick. Visualising data flows/transforms in programming too. Also, human languages... once you've grafted a nice base of 1000+ words and basic grammar, and your brain starts just soaking up more and more meaning as you hear it spoken, it's delicious.
Once you "get" what a double or triple integral is "doing", its just... really cool. I dunno why. I think because you get this kind of kinesthetic feel for this infinite sum of infinitesmal slivers of this abstract shape... makes my brain happy.
Or when you do integrals in polar co-ordinates, and you realise the integral is adding up these tiny elements of surface area, rotated around a point on the axis, and then that happening for every point on the axis and being summed along the shape... haha. It's like a weird brain massage.
It's that marrying of the hard analytical solution with the "aha!" of visualising the dynamics and the geometry. Something about that is cool.
Then again, I think lots of things can give you that same "aha!" kick. Visualising data flows/transforms in programming too. Also, human languages... once you've grafted a nice base of 1000+ words and basic grammar, and your brain starts just soaking up more and more meaning as you hear it spoken, it's delicious.