4 ms·

What makes this a four-point egg if only the first three points are required to derive the rest of the shape?

burkaman 3y ago
See Figure 15 on page 8: https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf https://web.archive.org/web/20200618202007/https://www.dynam... The egg is constructed of four distinct arcs based on four different points, plus two of them mirrored.
- rantallion 3y ago
  Thanks. This makes more sense. I was curious why the _inner_ point mattered, when the fourth point is actually the one on the side.
  - eduhetxub 3y ago
    I don't know exactly what you mean, but the name of this shape is consistent with the naming of traditional geometric constructions like the "five-centered arch" and the "three-centered arch" (see many diagrams online for details of these constructions). So "four-centered egg" might make more sense to you, though it could also be called the "six-centered egg", because it includes both sides, unlike the classical arch constructions.
a_t48 3y ago
There are four points inside the egg.
kazinator 3y ago
Also, why do we say "four legged table" in reference to common, rectangular tables? The position of the fourth leg is determined from the other three, so it shouldn't count!
- rantallion 3y ago
  I'd love to see a three-legged table stand up with the fourth corner under load.
  - kazinator 3y ago
    It has a leg there; it's just called a three legged table, because one of the legs is geometrically implied by the other three.
    - SamBam 3y ago
      Surely you only need two, as you could use two diagonal legs. Let's see if the name "two-legged table" takes off.
      - lupire 3y ago
        You only need 1 center leg.
    - dylan604 3y ago
      my grandfather was a custom cabinet builder, and for whatever reason 4 legged tables were his absolute nemesis. i have the last remaining 3 legged table of his. it's a round table, so i thought the 3 legs were a design choice. that notion was corrected when my dad started laughing at remembering his dad's sheer frustration when he realized 3 of 4 table legs were the same length...on multiple occasions.
      - kazinator 3y ago
        Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor.
        addaon 3y ago
        > Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor. Unless you're able to rotate it: https://www.scientificamerican.com/article/strange-but-true-turning https://www.scientificamerican.com/article/strange-but-true-...
gowld 3y ago
The Wikipedia article about the 2-point (Moss) egg (3 points derived from 2 freely chosen points) cites Freyja's article https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf https://web.archive.org/web/20200618202007/https://www.dynam... which has a 2-point (Moss) egg, a 4-point egg, and a 5-point egg. The OP article has only the 4-point egg.
- fanf2 3y ago
  Moss’s egg is a 3 point egg: it has 4 arcs, two of which are a mirrored pair.
SamBam 3y ago
Only the very first circle is needed to derive the rest of the shape. So that's a point and a radius, or two points.
- nick238 3y ago
  Two points (x1, y1, x2, y2) or 4 total parameters (x, y, rotation, scale) assuming you're using the exact shape provided, but from the interactive egg you can free the location/angles that they used for construction so you can wind up with less egg-like 4-point eggs. In the interactive link provided, you control the positions of 4 circle centers, each restricted along one of the axes. So you're giving 4 parameters (which also gives scale), and after including x-y offsets and rotation, it's 7 total numbers to make an arbitrary '4-point' egg anywhere in the plane
- lupire 3y ago
  That's for a specific case of 4-point egg. The points can be moved to make different egg shapes. The OP links to an interactive app.
samstave 3y ago
It looks like the four-point egg is defined by 8 circles, and connecting the intersections, of which their are four pair. Im just surprised the author never once used the proper term for the "west" "north" points; Quadrant. Its even the name for the snap function in all snap menus.
- fanf2 3y ago
  A quadrant is a quarter of a planar shape, not a point.

See Figure 15 on page 8: https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf https://web.archive.org/web/20200618202007/https://www.dynam... The egg is constructed of four distinct arcs based on four different points, plus two of them mirrored.

rantallion 3y ago
Thanks. This makes more sense. I was curious why the _inner_ point mattered, when the fourth point is actually the one on the side.
- eduhetxub 3y ago
  I don't know exactly what you mean, but the name of this shape is consistent with the naming of traditional geometric constructions like the "five-centered arch" and the "three-centered arch" (see many diagrams online for details of these constructions). So "four-centered egg" might make more sense to you, though it could also be called the "six-centered egg", because it includes both sides, unlike the classical arch constructions.

a_t48 3y ago

There are four points inside the egg.

kazinator 3y ago

Also, why do we say "four legged table" in reference to common, rectangular tables? The position of the fourth leg is determined from the other three, so it shouldn't count!

rantallion 3y ago
I'd love to see a three-legged table stand up with the fourth corner under load.
- kazinator 3y ago
  It has a leg there; it's just called a three legged table, because one of the legs is geometrically implied by the other three.
  - SamBam 3y ago
    Surely you only need two, as you could use two diagonal legs. Let's see if the name "two-legged table" takes off.
    - lupire 3y ago
      You only need 1 center leg.
  - dylan604 3y ago
    my grandfather was a custom cabinet builder, and for whatever reason 4 legged tables were his absolute nemesis. i have the last remaining 3 legged table of his. it's a round table, so i thought the 3 legs were a design choice. that notion was corrected when my dad started laughing at remembering his dad's sheer frustration when he realized 3 of 4 table legs were the same length...on multiple occasions.
    - kazinator 3y ago
      Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor.
      - addaon 3y ago
        > Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor. Unless you're able to rotate it: https://www.scientificamerican.com/article/strange-but-true-turning https://www.scientificamerican.com/article/strange-but-true-...

gowld 3y ago

The Wikipedia article about the 2-point (Moss) egg (3 points derived from 2 freely chosen points) cites Freyja's article https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf https://web.archive.org/web/20200618202007/https://www.dynam... which has a 2-point (Moss) egg, a 4-point egg, and a 5-point egg. The OP article has only the 4-point egg.

fanf2 3y ago
Moss’s egg is a 3 point egg: it has 4 arcs, two of which are a mirrored pair.

SamBam 3y ago

Only the very first circle is needed to derive the rest of the shape. So that's a point and a radius, or two points.

nick238 3y ago
Two points (x1, y1, x2, y2) or 4 total parameters (x, y, rotation, scale) assuming you're using the exact shape provided, but from the interactive egg you can free the location/angles that they used for construction so you can wind up with less egg-like 4-point eggs. In the interactive link provided, you control the positions of 4 circle centers, each restricted along one of the axes. So you're giving 4 parameters (which also gives scale), and after including x-y offsets and rotation, it's 7 total numbers to make an arbitrary '4-point' egg anywhere in the plane
lupire 3y ago
That's for a specific case of 4-point egg. The points can be moved to make different egg shapes. The OP links to an interactive app.

samstave 3y ago

It looks like the four-point egg is defined by 8 circles, and connecting the intersections, of which their are four pair. Im just surprised the author never once used the proper term for the "west" "north" points; Quadrant. Its even the name for the snap function in all snap menus.

fanf2 3y ago
A quadrant is a quarter of a planar shape, not a point.