I really appreciate the addition of the scale, it really adds to the intuition and understanding of how these graphs change, particularly with the rotations, I think the speed of contraction and expansion is non-linear, it looks like it might be due to variable absolute values with different shapes. This is just a "feeling" but the square seemed to be most variable in speed of expansion and contraction, and that kind of makes sense as it aligns with the axes of the 2d plane (complex plane), so all of the maximum absolute values lie on the axes and exactly half way between the axes at the same time in the rotation.
4:40 it starts looking like an isometric viewport. Its like those 3d printed hyperboloid toys where it has a turntrable with a stick leaning on an angle. They all seem to trace out a hyperboloid in isometric view, actually.
If a pentagon is a 5-gon, then the cubed pentagon is a 5/3-gon. The fifth power of the pentagon would be a 5/5-gon or just a 1-gon, but maybe you would consider the 5/5-gon to be 5 1-gons, one for each vertex of the 5-gon.
Watching my videos and leaving comments is a great support, so I thank you for that! If you want to show extra support, you can become a member of the channel: th-cam.com/channels/JZt93WO-evfsfi7YlVmrQA.htmljoin
I came up with thee pentagon cubed in middle school, thinking I had invented something new
maybe you did, and this guy invented it second.
To be clear I'm not claiming to have invented this idea, I just wrote a program to create some nice pictures!
@@TheGrayCuberhave you shared on GitHub / GotLab? I would love to contribute to this marvel *_*
I really appreciate the addition of the scale, it really adds to the intuition and understanding of how these graphs change, particularly with the rotations, I think the speed of contraction and expansion is non-linear, it looks like it might be due to variable absolute values with different shapes. This is just a "feeling" but the square seemed to be most variable in speed of expansion and contraction, and that kind of makes sense as it aligns with the axes of the 2d plane (complex plane), so all of the maximum absolute values lie on the axes and exactly half way between the axes at the same time in the rotation.
this is just great, thanks
6:18 That looks backwards: F_1(-1) = 1, F_2(-1) = -1, F_3(-1) = 2, F_4(-1) = -3, etc.
Wow what an oversight. Thank you for pointing this out!
Holy Universe, what a pleasant diction you have.
4:40 it starts looking like an isometric viewport. Its like those 3d printed hyperboloid toys where it has a turntrable with a stick leaning on an angle. They all seem to trace out a hyperboloid in isometric view, actually.
Ok you are just too much underrated.
I love your work!
But I suggest you to buy a better microphone.
3:37 I hate this. It breaks my brain.
Great job
This really reminds me of polar inversions :)
This is so beautiful
The hexagon squared looks like a Reuleaux triangle, but it'd be crazy if that's the exact curve.
If a pentagon is a 5-gon, then the cubed pentagon is a 5/3-gon. The fifth power of the pentagon would be a 5/5-gon or just a 1-gon, but maybe you would consider the 5/5-gon to be 5 1-gons, one for each vertex of the 5-gon.
when I saw "pentagon cubed" in the title I thought this was going to be about 6 dimensional trioprisms, like the cartesian product of three pentagons
First
"Feed a fed horse" haha I unironically love these corny vegan substitutes of idioms. I use "feed two birds with one scone" all the time.
This is such wonderful work. Do you have a way that your fans can help support you?! This video and.yoir website are such a gift!!
Watching my videos and leaving comments is a great support, so I thank you for that! If you want to show extra support, you can become a member of the channel: th-cam.com/channels/JZt93WO-evfsfi7YlVmrQA.htmljoin