3 ms·

Also known as a "squircle", https://en.wikipedia.org/wiki/Squircle https://en.wikipedia.org/wiki/Squircle, which is a way better name.

russellbeattie 2y ago
Oh, I disagree entirely! This name makes you think of alternate dimensions and other cool stuff. Sadly, maxisuperhyperbola and ultramaxisuperhyperbola don't seem to be things.
- mitthrowaway2 2y ago
  Since a hypercube is a higher-dimensional cube, I think a higher-dimensional hyperbola would be a "hyperhyperbola".
  - itishappy 2y ago
    hyperboloid, my day is ruined https://en.wikipedia.org/wiki/Hyperboloid https://en.wikipedia.org/wiki/Hyperboloid
    - adrian_b 2y ago
      "Hyperboloid" is a modern name. Since Archimedes until and including Euler, paraboloids and hyperboloids of 2 sheets were named "conoids" (parabolic conoids and hyperbolic conoids), which makes more sense than "hyperboloid", because they look like rounded cones (Archimedes analyzed only their variants that are surfaces of revolution). The hyperboloid of 1 sheet has been named by its discoverer (Christopher Wren) as "hyperbolical cylindroid", which is also more suggestive of the shape of this surface. The change in terminology to paraboloids and hyperboloids was justified by the fact that in the older literature "conoids" and "cylindroids" had been used only for surfaces of revolution, because those with elliptical sections were not discussed before Euler, but this justification fails, because we now also talk about elliptical cylinders and cones, so there the names "cylinder" and "cone" have been retained, even if they also referred strictly to surfaces of revolution in the older literature. A more consistent terminology would have been to retain the names "spheroid", "cylindroid" and "conoid" that were used in the old literature and add "elliptical" whenever they are not surfaces of revolution, like it has been done for "cylinder" and "cone".
jihadjihad 2y ago
The author of TFA has a couple neat posts about squircles that might be of interest, too: 0: https://www.johndcook.com/blog/2018/02/13/squircle-curvature/ https://www.johndcook.com/blog/2018/02/13/squircle-curvature... 1: https://www.johndcook.com/blog/2019/04/02/history-of-the-term-squircle/ https://www.johndcook.com/blog/2019/04/02/history-of-the-ter...
alex-robbins 2y ago
A superellipse is only a squircle if a and b are 1. As with squares and rectangles, all squircles are superellipses but not all superellipses are squircles.
- adharmad 2y ago
  Unrelated but on the topic of squircles, an interesting factoid: Among all squircles having arbitrary exponents (|x|^p + |y|^p = 1), PI (3.14159...) is the smallest value of ratio of circumference to diameter. There is a paper on this with the pithy title "π is the Minimum Value for Pi": https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11974122 https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11...
- kretaceous 2y ago
  > if a and b are 1 If a and b are equal* (not just 1). A circle is a special case of ellipse where a and b are equal and the eccentricity is 0. This is the same principle.
hnuser123456 2y ago
I think the novelty of the article was in the 2nd image, and why it's so much less well known. But my theory is there are not as many applications for symmetrical curvy lines that diverge than symmetrical curvy lines that converge.
- nlawalker 2y ago
  Yeah that bit was funny to me. "I'm not sure why closed shapes are so ubiquitous and pairs of diverging lines aren't."

russellbeattie 2y ago

Oh, I disagree entirely! This name makes you think of alternate dimensions and other cool stuff. Sadly, maxisuperhyperbola and ultramaxisuperhyperbola don't seem to be things.

mitthrowaway2 2y ago
Since a hypercube is a higher-dimensional cube, I think a higher-dimensional hyperbola would be a "hyperhyperbola".
- itishappy 2y ago
  hyperboloid, my day is ruined https://en.wikipedia.org/wiki/Hyperboloid https://en.wikipedia.org/wiki/Hyperboloid
  - adrian_b 2y ago
    "Hyperboloid" is a modern name. Since Archimedes until and including Euler, paraboloids and hyperboloids of 2 sheets were named "conoids" (parabolic conoids and hyperbolic conoids), which makes more sense than "hyperboloid", because they look like rounded cones (Archimedes analyzed only their variants that are surfaces of revolution). The hyperboloid of 1 sheet has been named by its discoverer (Christopher Wren) as "hyperbolical cylindroid", which is also more suggestive of the shape of this surface. The change in terminology to paraboloids and hyperboloids was justified by the fact that in the older literature "conoids" and "cylindroids" had been used only for surfaces of revolution, because those with elliptical sections were not discussed before Euler, but this justification fails, because we now also talk about elliptical cylinders and cones, so there the names "cylinder" and "cone" have been retained, even if they also referred strictly to surfaces of revolution in the older literature. A more consistent terminology would have been to retain the names "spheroid", "cylindroid" and "conoid" that were used in the old literature and add "elliptical" whenever they are not surfaces of revolution, like it has been done for "cylinder" and "cone".

jihadjihad 2y ago

The author of TFA has a couple neat posts about squircles that might be of interest, too: 0: https://www.johndcook.com/blog/2018/02/13/squircle-curvature/ https://www.johndcook.com/blog/2018/02/13/squircle-curvature... 1: https://www.johndcook.com/blog/2019/04/02/history-of-the-term-squircle/ https://www.johndcook.com/blog/2019/04/02/history-of-the-ter...

alex-robbins 2y ago

A superellipse is only a squircle if a and b are 1. As with squares and rectangles, all squircles are superellipses but not all superellipses are squircles.

adharmad 2y ago
Unrelated but on the topic of squircles, an interesting factoid: Among all squircles having arbitrary exponents (|x|^p + |y|^p = 1), PI (3.14159...) is the smallest value of ratio of circumference to diameter. There is a paper on this with the pithy title "π is the Minimum Value for Pi": https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11974122 https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11...
kretaceous 2y ago
> if a and b are 1 If a and b are equal* (not just 1). A circle is a special case of ellipse where a and b are equal and the eccentricity is 0. This is the same principle.

hnuser123456 2y ago

I think the novelty of the article was in the 2nd image, and why it's so much less well known. But my theory is there are not as many applications for symmetrical curvy lines that diverge than symmetrical curvy lines that converge.

nlawalker 2y ago
Yeah that bit was funny to me. "I'm not sure why closed shapes are so ubiquitous and pairs of diverging lines aren't."