You can actually take a pyramid with a square at the base with a height of half the side of the square. Then (try it yourself) build a cube with 6 such pyramids. If the side is a, the volume of the cube is a³. One pyramid is V = a³/6 = a²h/3. Now, intuitively, the shape of the base shouldn't change the volume, only the area would. That's an intuitive way of justifying where 3 comes from without integrals. More rigorously, you can stretch the pyramid to any height, which is a linear map that would increase the volume by a factor of h' / h, so the formula for V still stands. You can also move the top of a pyramid, which is a shear mapping so it doesnt change the volume (determinant = 1). Obviously, the mapping doesnt change a and h. Now, you can approximate a cone with any shape of the base with such pyramids which yields V = 1/3 S h
Audio needs improvement and if possible, try to show visually how the change in equation affects the shape or whatever the topic is. I hope i could explain the second part properly. Good video otherwise
the animation is really "3 blue 1 brown" esque
He made his editing program public recently I believe
@@SaesarCaladit's been public for ages afaik, just more popular recently
Thats because he used manim i think
The visuals are cool
You can actually take a pyramid with a square at the base with a height of half the side of the square. Then (try it yourself) build a cube with 6 such pyramids. If the side is a, the volume of the cube is a³. One pyramid is V = a³/6 = a²h/3.
Now, intuitively, the shape of the base shouldn't change the volume, only the area would. That's an intuitive way of justifying where 3 comes from without integrals.
More rigorously, you can stretch the pyramid to any height, which is a linear map that would increase the volume by a factor of h' / h, so the formula for V still stands.
You can also move the top of a pyramid, which is a shear mapping so it doesnt change the volume (determinant = 1). Obviously, the mapping doesnt change a and h.
Now, you can approximate a cone with any shape of the base with such pyramids which yields V = 1/3 S h
I would've loved to go into more depth with the geometric proof but animating in 3D was a bit of a nightmare. You have a good explanation.
I understood it, but still find it too fast for me.
Good video tho, keep it up.
Please provide Source Code in description.
Soo cool!!!
Hey bro ur videos are really good but consider investing in a better mic or atleast try to filter some noise in audacity
True, I have a budget setup. I can't really buy anything yet but I'm glad you like my videos.
@@pihedronI have the FiFine k669b it's a 20$ mic and with audacity it sounds just as good as a 150$ one good luck bro
Are you make the video with manim?
Yes.
Audio needs improvement and if possible, try to show visually how the change in equation affects the shape or whatever the topic is. I hope i could explain the second part properly.
Good video otherwise
That's good 👍