Discussion:
first shape discovered by a computer
(too old to reply)
sobriquet
2024-08-21 05:55:08 UTC
Permalink
Hi!

https://www.desmos.com/3d/t5fsaljsmh

The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
Chris M. Thomasson
2024-08-21 06:33:29 UTC
Permalink
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each vertex
connected to two points, at (0, 0, -1) and (0, 0, 1)?
Chris M. Thomasson
2024-08-21 06:36:40 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each vertex
connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz plane
rotated by pi / 2. I need to take a closer look and try to recreate it
on my end. Fun. Thanks for the post. Might have some more time tonight.
sobriquet
2024-08-21 12:20:47 UTC
Permalink
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz plane
rotated by pi / 2. I need to take a closer look and try to recreate it
on my end. Fun. Thanks for the post. Might have some more time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices on
the unit sphere.

I got the coordinates for the vertices from the paper referenced in the
recent Matt Parker video about the shape.



https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf


When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.

https://www.desmos.com/calculator/stjrx6qsxt
sobriquet
2024-08-21 13:29:26 UTC
Permalink
Post by sobriquet
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties,
but they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz
plane rotated by pi / 2. I need to take a closer look and try to
recreate it on my end. Fun. Thanks for the post. Might have some more
time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices on
the unit sphere.
I got the coordinates for the vertices from the paper referenced in the
recent Matt Parker video about the shape.
http://youtu.be/XZy3rXr2yeM
https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.
https://www.desmos.com/calculator/stjrx6qsxt
I think I got the exact coordinates for the vertices now.

https://www.desmos.com/3d/xaxwkqwgw3
Chris M. Thomasson
2024-08-21 19:31:18 UTC
Permalink
Post by sobriquet
Post by sobriquet
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties,
but they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz
plane rotated by pi / 2. I need to take a closer look and try to
recreate it on my end. Fun. Thanks for the post. Might have some more
time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices
on the unit sphere.
I got the coordinates for the vertices from the paper referenced in
the recent Matt Parker video about the shape.
http://youtu.be/XZy3rXr2yeM
https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.
https://www.desmos.com/calculator/stjrx6qsxt
I think I got the exact coordinates for the vertices now.
https://www.desmos.com/3d/xaxwkqwgw3
Cool! Thanks Man. :^)
Chris M. Thomasson
2024-08-23 21:38:40 UTC
Permalink
On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
[...]

A fun result from one of my experiments on this shape:

Loading Image...

;^D
sobriquet
2024-08-24 00:48:11 UTC
Permalink
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.

I'm back to exploring the Farey sequence.

https://www.desmos.com/calculator/m5ipzp6hv7
Chris M. Thomasson
2024-08-27 04:00:35 UTC
Permalink
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields... Can
you see/use this 360?

https://www.facebook.com/photo?fbid=1227714741720855

https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
sobriquet
2024-08-28 00:10:53 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields... Can
you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?

Facebook is an incredibly retarded website and generally unsuitable for
sharing content. If people are not on facebook, they can't even see
stuff on facebook.
sobriquet
2024-08-28 00:15:48 UTC
Permalink
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields...
Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable for
sharing content. If people are not on facebook, they can't even see
stuff on facebook.
I mean.. compare that to desmos.. not just is anyone able to see
anything you create on desmos and share with others, regardless of
whether they have a desmos account or not. People can even create stuff
and share it on desmos and desmos will not require you to make a desmos
account to do that.
Chris M. Thomasson
2024-08-28 19:03:25 UTC
Permalink
Post by sobriquet
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields...
Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?

YouTube is pretty nice:


Post by sobriquet
I mean.. compare that to desmos.. not just is anyone able to see
anything you create on desmos and share with others, regardless of
whether they have a desmos account or not. People can even create stuff
and share it on desmos and desmos will not require you to make a desmos
account to do that.
sobriquet
2024-08-28 19:35:04 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields...
Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
Yes, you can test it yourself. Log out from facebook (or use a different
browser that doesn't have your account info) and see if you can view
something you've shared on facebook (ensuring you've shared it globally
and not just with your fb friends).
Post by Chris M. Thomasson
http://youtu.be/-PUmt7i3zw4
Youtube is much better than facebook in that respect.
Post by Chris M. Thomasson
Post by sobriquet
I mean.. compare that to desmos.. not just is anyone able to see
anything you create on desmos and share with others, regardless of
whether they have a desmos account or not. People can even create
stuff and share it on desmos and desmos will not require you to make a
desmos account to do that.
Chris M. Thomasson
2024-08-28 19:40:36 UTC
Permalink
On 8/28/2024 12:35 PM, sobriquet wrote:
[...]
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
Yes, you can test it yourself. Log out from facebook (or use a different
browser that doesn't have your account info) and see if you can view
something you've shared on facebook (ensuring you've shared it globally
and not just with your fb friends).
It works fine for me:

Loading Image...

[...]
FromTheRafters
2024-08-28 19:42:22 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about fields... Can
you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable for
sharing content. If people are not on facebook, they can't even see stuff
on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign
in, but you can easily get around that just to view something.
Chris M. Thomasson
2024-08-28 19:47:39 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about
fields... Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign in,
but you can easily get around that just to view something.
Right. It even lets me look around in the 360:

Loading Image...
sobriquet
2024-08-29 01:26:48 UTC
Permalink
Post by Chris M. Thomasson
Post by FromTheRafters
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about
fields... Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign
in, but you can easily get around that just to view something.
https://i.ibb.co/FDmNGby/image.png
Yeah, I was wrong about that. It does first ask to sign in, but you can
click that popup away and then you can view the content even when not
logged in to facebook.
Ross Finlayson
2024-08-28 23:52:59 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about
fields... Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign in,
but you can easily get around that just to view something.
Ew, gross.

I think by FB you mean this "FaceBook" which is
entirely abused by all these "Ad-Mods" and
"Facebook Pros" who entirely abuse their peers
after writing a little note that it's for research
or for herding students or some other stated group,
who entirely abuse the system and its perceived
adherence to stated claims of content protections
and who are muchly the worst sort of users, abusers.

That one?
Chris M. Thomasson
2024-08-29 01:21:28 UTC
Permalink
Post by Ross Finlayson
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about
fields... Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign in,
but you can easily get around that just to view something.
Ew, gross.
I might be misunderstanding you, but the damn FB is The FB. It does ask
you to login... However, it can be discarded and then you can see the
content. Fair enough?
Post by Ross Finlayson
I think by FB you mean this "FaceBook" which is
entirely abused by all these "Ad-Mods" and
"Facebook Pros" who entirely abuse their peers
after writing a little note that it's for research
or for herding students or some other stated group,
who entirely abuse the system and its perceived
adherence to stated claims of content protections
and who are muchly the worst sort of users, abusers.
That one?
FromTheRafters
2024-08-29 10:42:25 UTC
Permalink
Post by Ross Finlayson
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
[...]
https://i.ibb.co/zfYXsLz/ct-p1.png
;^D
Yeah.. geometry is fun.
I'm back to exploring the Farey sequence.
https://www.desmos.com/calculator/m5ipzp6hv7
Nice. For some reason this thread made my mind think about
fields... Can you see/use this 360?
https://www.facebook.com/photo?fbid=1227714741720855
https://www.facebook.com/share/p/hQrh2XkHM9VvrRWJ
Ask chatgpt how facebook works?
Facebook is an incredibly retarded website and generally unsuitable
for sharing content. If people are not on facebook, they can't even
see stuff on facebook.
Are you 100% sure about that? Even if the content is marked as public?
I have no FB account and I have seen FB content. It asks you to sign in,
but you can easily get around that just to view something.
Ew, gross.
I think by FB you mean this "FaceBook" which is
entirely abused by all these "Ad-Mods" and
"Facebook Pros" who entirely abuse their peers
after writing a little note that it's for research
or for herding students or some other stated group,
who entirely abuse the system and its perceived
adherence to stated claims of content protections
and who are muchly the worst sort of users, abusers.
That one?
Yep, that's the one! What was your first hint?

Chris M. Thomasson
2024-08-23 05:05:10 UTC
Permalink
Post by sobriquet
Post by sobriquet
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties,
but they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz
plane rotated by pi / 2. I need to take a closer look and try to
recreate it on my end. Fun. Thanks for the post. Might have some more
time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices
on the unit sphere.
I got the coordinates for the vertices from the paper referenced in
the recent Matt Parker video about the shape.
http://youtu.be/XZy3rXr2yeM
https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.
https://www.desmos.com/calculator/stjrx6qsxt
I think I got the exact coordinates for the vertices now.
https://www.desmos.com/3d/xaxwkqwgw3
This view looks very interesting to me:

https://ibb.co/NyjFyhc

It looks like two pentagons:

Loading Image...

I need to bust out my plotter and try rotating a normalized unit
pentagon. I "think" I see what is going on here. Humm. Might come up
with some new shapes along the way. ;^D
Chris M. Thomasson
2024-08-21 19:30:59 UTC
Permalink
Post by sobriquet
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties,
but they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz
plane rotated by pi / 2. I need to take a closer look and try to
recreate it on my end. Fun. Thanks for the post. Might have some more
time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices on
the unit sphere.
I got the coordinates for the vertices from the paper referenced in the
recent Matt Parker video about the shape.
http://youtu.be/XZy3rXr2yeM
https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.
https://www.desmos.com/calculator/stjrx6qsxt
Okay. Well, the fun part is that I can use it to plot one of my
experiential 3d von Kochs on. My algorithm uses a single triangle to do
its thing. Here is an older low-res example:


Chris M. Thomasson
2024-08-21 20:13:53 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Post by Chris M. Thomasson
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties,
but they all appear to have the same volume.
It looks like a unit 5-gon in the xy plane at (x, y, 0) with each
vertex connected to two points, at (0, 0, -1) and (0, 0, 1)?
Not quite... Like two 5 gons one on the xy plane and one on the xz
plane rotated by pi / 2. I need to take a closer look and try to
recreate it on my end. Fun. Thanks for the post. Might have some more
time tonight.
It's the shape with the biggest volume one can obtain with 8 vertices
on the unit sphere.
I got the coordinates for the vertices from the paper referenced in
the recent Matt Parker video about the shape.
http://youtu.be/XZy3rXr2yeM
https://www.ams.org/journals/mcom/1963-17-082/S0025-5718-63-99183-X/S0025-5718-63-99183-X.pdf
When I computed the volume of the shape that has an isosceles
triangle as the base for the pyramid, it seemed to give the
impression that it's a twelfth of the total volume, implying
that the other pyramid shape with a scalene triangle base has
the same volume.
https://www.desmos.com/calculator/stjrx6qsxt
Okay. Well, the fun part is that I can use it to plot one of my
experiential 3d von Kochs on. My algorithm uses a single triangle to do
http://youtu.be/AIrP4KeSIjI
Or even one like this, from an older fractal of mine that loves
triangles... ;^)

Loading Image...
Chris M. Thomasson
2024-08-23 05:36:13 UTC
Permalink
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
Not this one. I need to experiment some more:

Loading Image...
Chris M. Thomasson
2024-08-23 06:29:42 UTC
Permalink
Post by Chris M. Thomasson
Post by sobriquet
Hi!
https://www.desmos.com/3d/t5fsaljsmh
The shape is comprised of 12 pyramids that come in two varieties, but
they all appear to have the same volume.
https://i.ibb.co/tQnV6zL/ct-pov.png
Not this one either:

Loading Image...
Loading...