Spherical Coordinates 3D Animation
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- Опубліковано 14 січ 2025
- This section can be a little hard to visualize in 2D. This video should help you to visualize spherical coordinates and set up the bounds of integration for triple integrals.
Paul's Math Notes: tutorial.math.l...
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 :)
@@XYZandRGBhow do you go about animating things like this ?
@@tommygstonymec I use Blender. I build all of the pieces you see in the video and vary their rotation and size and position using keyframes.
hmm
Maybe in the future generations they will use now animation or graphical representations using new technologies
A good teacher is one who can make complicated topics the most easiest ones. Thank you
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
Thanks dude saved my brains from frying
Thank you so much, something stuck in my mind for more than 4 hours about this because the teacher at my university just talk about this for 5 minutes then solve 2 problems in 10 minutes so I do not understand enough but you know what not just me but also other students in my class but at the end they are still able to get 9 or even 10 at the exam, but I believe that not many of them know clearly about this, that is so sad about education when someone does not fully understand something and can get a 10 grade but others have to mine and understand deeply which costs a lot of time but in God I trust, the time I spend for math is not worthless. THANK YOU SO MUCH FOR YOUR LECTURE. God blessed you.
@@wonbpoly Once you start to apply this knowledge, you will see the benefit of truly understanding the concepts, and will be helping your peers.
This is gold for spherical coordinates. Thank you!
Animations help a LOT. This video made the concept crystal clear to me. Thank you!
Sending you all the best wishes, being able to explain difficult concepts easily is what marks a great educator. Thank you!
Thank you very much, i have an exam in an hour and finally understand about all of this
ty for everything, my friend saw your video and he say he gonna take 5 in the impossible test tomorow, god bless him and all the students
I have never understood the spherical φ coordinate and how it only goes to π and not 2π until i watched this video, THANKS A LOT
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 video. Cleared all my doubts. Thank you so much for this! 😁
this is marvelous effort to teach coordinates.
finally I understood why the phi angle is between 0 to 180 degree in the spherical coordinate system. thank you sooooo much !!
i have a re-exam and now phi is much more intuitive than the first time!! Thanks very very much for such a good explanation!!!!
Thanks so much for making this video. Unique and super helpful visualization!
I actually appreciate your time, I had finally learnt.
Thank you very much. It might have took some effort to make this video, I am grateful for this.
dude you're the boss, thank you !!
understood in a very easy way ...because you took lot of hard pain to do it. thanks a lot
For the first time I understood this
Finally❤
dude you're the best
I'm from INDIA Your video helped me a lot to make my concept crystal clear ❤
This video made me understand why theta is only from 0 to π, thanks!
did you mix up phi and theta? my notes and other videos show them the other way
It depends on which book you are using. There is no standard, but what I have in my video is what I've seen in Stewart calculus.
@@XYZandRGB its weird there is no standard. thanks
Nice video. I would recommend including the bounds and other numbers you're talking about on screen next time.
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.
very helpful video! i have a calculus coming up and you have no idea how this saved me hahah thanks a bunch 😊
Good luck on your exam!
this has been incredibly helpful, thank you!
thank you so much , had a seizure making sense out of this on my textbook , this video cleared alot , realy
5:50 can anyone explain why phi is not from pi to 3/2 pi
phi is measured from the top of the z axis. phi = 0 is the positive z-axis, and phi = pi is the negative z axis.
@@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?
Great video bro! I couldnt understand what phi is and now got it! Thank you!
Very informative and very well presented ,thank you
Thank you very much for the graph & explanation
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! 👏👏👏👏
Thanks so much for this video. It really clarified a few things for me.
finally a good video regarding this !!! thank you !!!
thank u so much you helped me a lot🌷💖
*Great explanation Sir. Thanks, lots of love from India*
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
this is brilliant, thank you for your work!!
Thank u so much Teacher Love from INDIA ❤
Awesome explaination
Short and simple but very helpful, thank you so much
wonderful
Can't theta be from π/2 to 3π/2 at 5:25 or it is same as π to 2π
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.
Remember that theta starts at the positive x-axis, just like polar coordinates. It's a little odd because it "looks" like it is starting on the left.
a really nice representation thank you
saved my calc grade thank you🙏
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.
Thanks
great video 🙌🏾👏🏾
Thank you so much! this made it so clear
Great video, keep up the good work!!
muchismas gracias por explicarlo todo bien! me ha ayudado mucho!
AMAZING IT WAS.... ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Very intuitve explanation. Thanks 💯
our professor is trying to teach this using a chalkboard its sooo frustrating,, thanku so much for posting this!
Thank you so much for sharing this video! It's very helpful!!
makes learning so interesting
Thank you very much. 🙏
as in polar coordinate 2d we needed an initial line and pole for frame of reference , i wonder if we need all the three axes here?
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.
thank you i've been trying forever to visualize phi
great animations, can I ask how they were created?
I made them using Blender, a free 3D software
very good visuals
Great video
Nice explanation
Great explanation sir
Thank you so much. You saved me
Thanks!
5:24 why theta limits are from pi to 2pi
Could you pls explain
Theta starts at the positive x axis, and moves toward the positive y axis, so it has to travel halfway around and start at pi.
Thank you so much :)
Thanks! This was extremely helpful :D
Very good
Is fie not clockwise?
"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
thank you!
AMAZING VIDEO THANK YOU SO MUCH
the lovely grease pencil :) I am also planning to use Blender to do math animations. It's gonna be fun. Subs.
I actually used this site. www.calligraphr.com/en/
but I will probably be using grease pencil for that in the future.
Keep the hard work up 👍
Thank you! Also why did you change your audio of Phi out lol
I mistakenly said "theta" instead a few times. Audio editing is not my strong suit :)
Thank you so much ❤
which software are you using ?
I used Blender. It's totally free to use!
The best🔥🔥🔥🔥🔥🔥
Thank you very much sir !!!
excellent👌👌
Thanks ☺️😍
excellent
Good
This was beautiful!! Thank you very much.
thank you for this animation!!
This helped me understand the Qubit
amazing. Thanks a lot.
Wow, this helped a lot. Thank you
awesome video!!
I need these animations! my prof's drawings are so hard to interpret
Thank you !!
Tnanks man
great video sir ... helped a lot
Thank you!! This was very informative
LEGEND
super helpful...thank u so much
Thank you