Spherical Coordinates 3D Animation

Рет қаралды 161,761

4 жыл бұрын

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.lamar.edu/Classe...

Пікірлер: 155

@Lexyvil 2 жыл бұрын

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...

@XYZandRGB 2 жыл бұрын

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 :)

@tommygstonymec Жыл бұрын

@@XYZandRGBhow do you go about animating things like this ?

@XYZandRGB Жыл бұрын

@@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.

@satwiknagulapati9377 10 ай бұрын

hmm

@ryemiranda6800 7 ай бұрын

Maybe in the future generations they will use now animation or graphical representations using new technologies

@hnybdgr-uc8mx 3 жыл бұрын

Thanks dude saved my brains from frying

@AnnmusPnda Жыл бұрын

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

@abdullahrafeq6733 14 күн бұрын

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!!!!

@user-vc8rw3pi2u 4 ай бұрын

A good teacher is one who can make complicated topics the most easiest ones. Thank you

@Mel-wq5in 27 күн бұрын

very helpful video! i have a calculus coming up and you have no idea how this saved me hahah thanks a bunch 😊

@XYZandRGB 26 күн бұрын

Good luck on your exam!

@corneliamorissa8266 3 жыл бұрын

Thank you very much, i have an exam in an hour and finally understand about all of this

@Chrisymcmb 2 жыл бұрын

This is gold for spherical coordinates. Thank you!

@AK-zz7sn Жыл бұрын

Animations help a LOT. This video made the concept crystal clear to me. Thank you!

@koala1578 Жыл бұрын

Sending you all the best wishes, being able to explain difficult concepts easily is what marks a great educator. Thank you!

@vinamrasinha6210 2 жыл бұрын

Great video. Cleared all my doubts. Thank you so much for this! 😁

@user-iv9zj4vu5k 9 ай бұрын

I actually appreciate your time, I had finally learnt.

@miltonvento8767 Жыл бұрын

Thanks so much for making this video. Unique and super helpful visualization!

@steveying1305 5 ай бұрын

This video made me understand why theta is only from 0 to π, thanks!

@xhx-ms6lv 7 ай бұрын

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.

@joshtalks88 Жыл бұрын

I'm from INDIA Your video helped me a lot to make my concept crystal clear ❤

@funnyboy7603 2 жыл бұрын

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

@yasmeenajan3955 Жыл бұрын

this is marvelous effort to teach coordinates.

@maheshnerlekar9791 2 жыл бұрын

understood in a very easy way ...because you took lot of hard pain to do it. thanks a lot

@ankitaaarya 2 жыл бұрын

Thank you very much. It might have took some effort to make this video, I am grateful for this.

@Randomation 7 ай бұрын

this has been incredibly helpful, thank you!

@Festus2022 2 жыл бұрын

Thanks so much for this video. It really clarified a few things for me.

@ahmetenesacar2326 2 жыл бұрын

Great video bro! I couldnt understand what phi is and now got it! Thank you!

@user-qp2ps1bk3b 4 ай бұрын

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

@amir5379 3 жыл бұрын

dude you're the boss, thank you !!

@arvindravindran8482 3 жыл бұрын

Very informative and very well presented ,thank you

@-__-kb5lx 9 ай бұрын

Short and simple but very helpful, thank you so much

@hou-yawang516 Жыл бұрын

Thank you so much for sharing this video! It's very helpful!!

@cloriscloris5491 3 жыл бұрын

Thank you very much for the graph & explanation

@vee.333k Жыл бұрын

our professor is trying to teach this using a chalkboard its sooo frustrating,, thanku so much for posting this!

@maheenkamran5258 4 ай бұрын

Thank you so much! this made it so clear

@parsasoli2015 27 күн бұрын

a really nice representation thank you

@chriskazakos9614 9 ай бұрын

Great video, keep up the good work!!

@silverspin 2 ай бұрын

Thanks! This was extremely helpful :D

@ANJA-mj1to 7 ай бұрын

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! 👏👏👏👏

@fadlialim8762 3 жыл бұрын

dude you're the best

@chAD6969 Жыл бұрын

Thank u so much Teacher Love from INDIA ❤

@horacioquiroga290 10 ай бұрын

saved my calc grade thank you🙏

@malefetsanekoalane4549 4 ай бұрын

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?

@XYZandRGB 4 ай бұрын

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.

@malefetsanekoalane4549 4 ай бұрын

Thanks

@korlagoutham3659 3 жыл бұрын

Awesome explaination

@derekdannaldson1906 Жыл бұрын

muchismas gracias por explicarlo todo bien! me ha ayudado mucho!

@Brekstahkid Жыл бұрын

Wow, this helped a lot. Thank you

@cindy_le1106 Жыл бұрын

Thank you!! This was very informative

@kiranjoseph3879 3 ай бұрын

Great explanation sir

@SamFriedman 3 жыл бұрын

Nice video. I would recommend including the bounds and other numbers you're talking about on screen next time.

@XYZandRGB 3 жыл бұрын

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.

@soylaafissa 2 жыл бұрын

thank u so much you helped me a lot🌷💖

@Cherry-bj7dd 3 жыл бұрын

Thank you so much. You saved me

@valentinaflores9043 3 ай бұрын

AMAZING VIDEO THANK YOU SO MUCH

@fareedabifarraj483 3 жыл бұрын

Keep the hard work up 👍

@darshanhollam4401 2 жыл бұрын

great video sir ... helped a lot

@marielcmlr Жыл бұрын

thank you for this animation!!

@sartajshabeer 2 жыл бұрын

great video 🙌🏾👏🏾

@salmaalmunayes4251 Жыл бұрын

very good visuals

@luckychouhan3393 2 жыл бұрын

Thank you very much 😍😍 !! Please sir make more videos on multivariable calculus 😇

@thamirisbalbi8053 Жыл бұрын

awesome video!!

@bathulalikith9026 3 жыл бұрын

Nice explanation

@LarryChen-bh8uo 29 күн бұрын

amazing video

@taladasandeep8497 3 жыл бұрын

Thank you very much sir !!!

@krittikasarkar6989 2 жыл бұрын

AMAZING IT WAS.... ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

@rs-tarxvfz 2 жыл бұрын

This helped me understand the Qubit

@Prammybattula Жыл бұрын

super helpful...thank u so much

@rohanverma704 2 жыл бұрын

amazing. Thanks a lot.

@zeinabashtab1456 2 жыл бұрын

wonderful

@PhoGa Жыл бұрын

Great video

@shivangsingh5834 2 жыл бұрын

cleared my doubt professor

@PM-xd6nv Жыл бұрын

This was beautiful!! Thank you very much.

@mohityadav151 Жыл бұрын

Thank you very much. 🙏

@user-xg8nr9ke3e 8 ай бұрын

Thank you so much ❤

@micahfullinfaw6998 2 жыл бұрын

I need these animations! my prof's drawings are so hard to interpret

@jamesacosta6090 3 жыл бұрын

Wow beautifuly explained

@zarrinnahid448 2 жыл бұрын

Thank you so much :)

@abdullahalangari2053 Жыл бұрын

Thank you !!

@drewtaylor6764 4 жыл бұрын

Thanks!

@arsalansyed4709 3 жыл бұрын

thank you!

@jlpsinde Жыл бұрын

Very good

@mostafaessamfreij9904 Жыл бұрын

excellent

@rajeshgiri8629 2 жыл бұрын

Nice video

@faroukelkiouas7828 3 жыл бұрын

The best🔥🔥🔥🔥🔥🔥

@user-jk2tp6gs2g 3 жыл бұрын

the lovely grease pencil :) I am also planning to use Blender to do math animations. It's gonna be fun. Subs.

@XYZandRGB 3 жыл бұрын

I actually used this site. www.calligraphr.com/en/ but I will probably be using grease pencil for that in the future.

@vaderanomaly1573 2 жыл бұрын

LEGEND

@theblitz1687 2 жыл бұрын

did you mix up phi and theta? my notes and other videos show them the other way

@XYZandRGB 2 жыл бұрын

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.

@theblitz1687 2 жыл бұрын

@@XYZandRGB its weird there is no standard. thanks

@VNFilmography 4 ай бұрын

Thank you

@onarollthough7380 2 ай бұрын

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.

@ElkhedrAli 3 жыл бұрын

Thanks ☺️😍

@user-kf5uz6rw4w 3 ай бұрын

that changing Rho from 0 < Rho

@arulananthams2540 7 ай бұрын

Subscribed❤

@nelsonsimukoko363 2 жыл бұрын

The last diagrams better u use the cursor to show us where u were starting from and ending when getting phi

@gerard-nagle Жыл бұрын

great animations, can I ask how they were created?

@XYZandRGB Жыл бұрын

I made them using Blender, a free 3D software

@rs-tarxvfz 2 жыл бұрын

Great video ! what is difference between Parametric and Cylindrical (r,theta,z)?

@XYZandRGB Жыл бұрын

Cylindrical is a coordinate system very similar to spherical that uses (r, theta, and z) like you mentioned. r is measured in the same way as polar coordinates. Parametric is pretty different, and is usually used to define curves that travel along a 3D surface, rather than the solid itself. They can be used together to define a curve. For example: r = 1, theta = t and z = t will give you a curve that will spiral up along the surface of a cylinder.

@culturecreating 4 ай бұрын

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?

@XYZandRGB 28 күн бұрын

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.

@jaybheart9767 2 жыл бұрын

Hello can i ask? Is it necessary to change the sign if we going to transform it to spherical coordinates?

@XYZandRGB Жыл бұрын

Since r is a radius and goes in all directions in the XY plane, we don't need to worry about positives and negatives that can result from being "above" or "below" the axis.

@han.ngoarchi 2 жыл бұрын

I don't know why my prof is switching the properties of phi and theta, I'm so confused.

@MathematicsZoneharshaarora 3 жыл бұрын

which software did you use to create animations?

@XYZandRGB 3 жыл бұрын

I used Blender. It's free and getting better every version

@nelsonsimukoko363 2 жыл бұрын

Good

@asagi0111 3 жыл бұрын

Thank you! Also why did you change your audio of Phi out lol

@XYZandRGB 3 жыл бұрын

I mistakenly said "theta" instead a few times. Audio editing is not my strong suit :)

@sword0825 Жыл бұрын

🔥🔥🔥🔥

@a7medz0 Жыл бұрын

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

@XYZandRGB Жыл бұрын

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.

@nakshatrasharma7183 3 жыл бұрын

Can't theta be from π/2 to 3π/2 at 5:25 or it is same as π to 2π

@RahulSharma-oc2qd 3 жыл бұрын

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.

@XYZandRGB 3 жыл бұрын

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.