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Comment by rantallion | Hacker News Reader

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

See Figure 15 on page 8: 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.

Thanks. This makes more sense. I was curious why the _inner_ point mattered, when the fourth point is actually the one on the side.

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.

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.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.

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

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.

A quadrant is a quarter of a planar shape, not a point.

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!

I'd love to see a three-legged table stand up with the fourth corner under load.

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.

Surely you only need two, as you could use two diagonal legs.

Let's see if the name "two-legged table" takes off.

You only need 1 center leg.

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.

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.

> 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-...

Wish I'd be able to rotate my floor instead.

There are ways:

(1) Diagonal legs that give the table a wide stance. Draw a triangle that the tabletop fits entirely inside of. The legs touch the ground at the vertices of the triangle.

(2) Make the table itself arbitrarily heavy. A downward force on the corner of the tabletop will create torque around an axis, and this torque wants to tip it over. But the table's center of mass is on the other side of this axis, and the table's weight creates torque too. If the table's mass is high enough, this torque is greater, and it won't tip.

(3) Screw the table to the floor. Is this a table? I think it's still a table. You often see tables attached to the floor.

(4) Make one leg really wide so that it stretches from one corner to the other. The other two legs can be traditional.

The table + load will tip over if the center of mass is vertically outside of the convex polygon formed by the tips of the legs (in this case a triangle); i.e. the base of the object.

Center of mass over base -> stable

Center of mass outside base -> capsize

why do we say a rectangle has four sides, when it's just 2 reflected

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.

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

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.

There are four points inside the egg.

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