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  • first shape discovered by a computer

    From sobriquet@21:1/5 to All on Wed Aug 21 07:55:08 2024
    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.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Aug 21 14:20:47 2024
    Op 21/08/2024 om 08:36 schreef Chris M. Thomasson:
    On 8/20/2024 11:33 PM, Chris M. Thomasson wrote:
    On 8/20/2024 10:55 PM, sobriquet wrote:

    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.youtube.com/watch?v=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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Aug 21 15:29:26 2024
    Op 21/08/2024 om 14:20 schreef sobriquet:
    Op 21/08/2024 om 08:36 schreef Chris M. Thomasson:
    On 8/20/2024 11:33 PM, Chris M. Thomasson wrote:
    On 8/20/2024 10:55 PM, sobriquet wrote:

    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.youtube.com/watch?v=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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Sat Aug 24 02:48:11 2024
    Op 23/08/2024 om 23:38 schreef Chris M. Thomasson:
    On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
    [...]

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

    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Aug 28 02:10:53 2024
    Op 27/08/2024 om 06:00 schreef Chris M. Thomasson:
    On 8/23/2024 5:48 PM, sobriquet wrote:
    Op 23/08/2024 om 23:38 schreef Chris M. Thomasson:
    On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
    [...]

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

    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.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Aug 28 02:15:48 2024
    Op 28/08/2024 om 02:10 schreef sobriquet:
    Op 27/08/2024 om 06:00 schreef Chris M. Thomasson:
    On 8/23/2024 5:48 PM, sobriquet wrote:
    Op 23/08/2024 om 23:38 schreef Chris M. Thomasson:
    On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
    [...]

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

    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.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Wed Aug 28 21:35:04 2024
    Op 28/08/2024 om 21:03 schreef Chris M. Thomasson:
    On 8/27/2024 5:15 PM, sobriquet wrote:
    Op 28/08/2024 om 02:10 schreef sobriquet:
    Op 27/08/2024 om 06:00 schreef Chris M. Thomasson:
    On 8/23/2024 5:48 PM, sobriquet wrote:
    Op 23/08/2024 om 23:38 schreef Chris M. Thomasson:
    On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
    [...]

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

    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).


    YouTube is pretty nice:

    https://youtu.be/-PUmt7i3zw4

    Youtube is much better than facebook in that respect.




    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.





    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Thu Aug 29 03:26:48 2024
    Op 28/08/2024 om 21:47 schreef Chris M. Thomasson:
    On 8/28/2024 12:42 PM, FromTheRafters wrote:
    Chris M. Thomasson wrote :
    On 8/27/2024 5:15 PM, sobriquet wrote:
    Op 28/08/2024 om 02:10 schreef sobriquet:
    Op 27/08/2024 om 06:00 schreef Chris M. Thomasson:
    On 8/23/2024 5:48 PM, sobriquet wrote:
    Op 23/08/2024 om 23:38 schreef Chris M. Thomasson:
    On 8/21/2024 12:31 PM, Chris M. Thomasson wrote:
    [...]

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

    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:

    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.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)