I don't understand why they don't teach this today at my university without using animations like these to help us visualize 3D shapes mentally. We have the technology now...
I feel the same way. I made this because I couldn't find something similar. Most of your professors learned it from chalkboard drawings, so don't be too upset if they try to teach you the same way :)
Thank's a ton for the animation man, it really helped, like fr. My prof isn't the best, she runs through the material like she's tryna speedrun the class
θ is to reduce the aggregate of three-dimensional space to a surface, Φ is to reduce the aggregate of a surface to a line, which is the intersection of the surface and the cone, and ρ is to reduce a line to a point. The positioning of any point in space can be completed.
Great animation.Thanks. You have my subscription. I think greatly of all the pre computer graphics mathematicians who could see it all in their heads.Makes one wonder? In the long run are our brains going to be less or more capable of visualisation?
That's such an interesting question. I feel like we are adding to the number of people that can visualize a topic each time we express it in a new way. There's no shortage of difficult concepts to understand, so I suppose anyone can still exercise the skill as much as they want. I had a colleague suggest that some boys gain an advantage in spatial visualization over girls from jumping off of playground equipment and tracking movements of the ball in sports more often. I have no idea if nature or nurture is the main culprit, but I suspect it's a skill that can be strengthened.
This was very concise! Illustrated fantastici! All important key features in order to calculate the transmitted irradience by angular dependent. Using Yours - presented coordinates and the following spherical coordinate system I can specify a given direction for the zenith and azimuth angles thus the transmittance of this system is a function of direction of incident radiation. So valuable information also for the irradience from the sun, sky and for all hemispheric areas given by the independent of changes in the sun or sky radiance. Thank you because performing an integration of the transmitted irradience and calculating the total radiant flux in civil engineering we can see better geometry for example water, glass, polarized elements, i. c. Also we can imply two-dimensional Fourier transform of Cartesian coordinates if we understand better first important step that implys in all disciplines not only engineering approach! 👏👏👏👏
thank you SO MUCH for this video. It got me unstuck. I didn't realize that the vertical angle goes only from 0 to Pi, not to 2Pi, like angles usually would
Thanks! Putting this (unfinished) video up was a little experiment to see if people would like this kind of video. Comments like yours motivate me to continue making them.
Changing the frame of reference from what I described here is a bit more advanced than what I can cover here, but I would assume we need all 3 axes to define a frame of reference.
So x and y axioms have an angular relationship and the z axioms phi is independent, having half the values because its the same on either side of the axis without concern with position. Hmm interesting stuff.
"fie" or phi originates from the positive z-axis, and it travels in all directions. To use an analogy, 11:00 and 1:00 on the clock would have the same phi value of 1 hour
theta is positive when it is measured counterclockwise rotation from x axis about z axis. I guess that might be the reason for it being in the range of π to 2π.
The question is when do we use normal triple integral(dz dy dz), triple integral in cylindrical coordinates (r dz dr dθ) or triple integral in spherical coordinates? is it based on the graph or there is a better way of knowing this ""Given that sometimes we encounter functions that are hard to graph
I would suggest using the coordinate system that has the most constants in its bounds. You can convert the equation you are integrating to any coordinate system you like, so it is usually based on the shape of the solid.
@@XYZandRGB i understand that, but if you consider anticlockwise it will go from pi to 3/2 pi and if you consider clockwise it will go from pi/2 to pi. i wonder if its correct both ways.
@@subhadip3679 The range of phi is defined as being from 0 to pi, so those are the only valid numbers for phi. Are you sure we're not talking about theta?
