# What is the official 2 sided object?

## Main Question or Discussion Point

A totally pointless question but it bugs me every time I try and put the round block through the square shaped holes.

A circle has one side, and equalateral triangle has three equal sides, square four, pentagon, hexagon, etc, etc,

Is there a two side shape in that group, or is the circle gate crashing the equal side party as it doesn't have a straight side?

May this should be in the philosophy section?

disregardthat
a line would have two straight sides, I don't know of any other figures that have that property. But then again, a line is not two dimensional.

StatusX
Homework Helper
There is always a graph consisting of n edges and n vertices. For n>=3, these can be arranged to look like polygons, and for n=1, like a circle. So however you want to arrange the graph with two edges and two vertices could qualify for what you want. One way would be like the side view of a lemon, another like the perimeter of half a circle. I don't see a natural choice, other than a circle where you arbitrarily define two halves of the curcumference to be different sides, even though there is no "corner" where they meet.

actually, the circle does *not* have 1 side. this is just weird mnemonic that kindergarten teachers like to "teach" their students for some reason or another.

if anything it has infinitely many sides, being the limit space of a sequence of regular polygons of increasing number of sides.

actually, the circle does *not* have 1 side. this is just weird mnemonic that kindergarten teachers like to "teach" their students for some reason or another.

if anything it has infinitely many sides, being the limit space of a sequence of regular polygons of increasing number of sides.
That does fit better as then you can have 2D shapes with equal sides numbered 3 to infinity. I assume 1 would be a dimensionless dot, and 2 would be a zero thickness line but they can't exist on a two dimensional plane.

Can you do the same thing with 3D objects, three sided pyramid (can't remember it's name) cube, do pentagons teselate, etc, etc, until you get to sphere made up of an infinitite number of infinite equal sided faces?

That does fit better as then you can have 2D shapes with equal sides numbered 3 to infinity. I assume 1 would be a dimensionless dot, and 2 would be a zero thickness line but they can't exist on a two dimensional plane.
this is an excellent example as to why mathematics is written the way it usually is. we want to be specific and accurate at the same time. to accomplish this, you might want to rephrase this whole inquiry as such:

given a finitely many set of points on the plane, what is the convex hull of those points? Is it possible for the boundary of the convex hull of these points to consist of two distinct line segments? If the convex hull has a nonzero area, what is the minimal possible number of points in the original set of points?

(if you don't know what "convex hull" means, look it up on wikipedia)

Can you do the same thing with 3D objects, three sided pyramid (can't remember it's name) cube, do pentagons teselate, etc, etc, until you get to sphere made up of an infinitite number of infinite equal sided faces?
In 3-space, we run into similar interesting questions. The tetrahedron has 4 sides, actually, not three. In fact, that's a good question: how many sides are possible for the boundary of the convex hull of finitiely many points in 3-space? (incidentally, Euler's Formula comes gliding into the room at this point of the inquiry, looking not a little like Veronica Lake)

Well I've spent an hour rearranging Euler's Formula and I can't get it looking like Veronica Lake.... but as I'm meant to be looking after baby panda I suppose I'll have to go back to showing how to get the triangular block through the round hole... I'll spend more time looking at the Veronica Lake problem after Mrs Panda has gone to bed though...

Well I've spent an hour rearranging Euler's Formula and I can't get it looking like Veronica Lake.... but as I'm meant to be looking after baby panda I suppose I'll have to go back to showing how to get the triangular block through the round hole... I'll spend more time looking at the Veronica Lake problem after Mrs Panda has gone to bed though...
Oh, wait, I meant Kim Basinger...

Anyway, that cryptic remark refers to the fact that Euler's Formula actually helps limit the number of faces, edges and vertices possible on a convex polyhedron (of finite area) in 3-space. For example, what happens if you try to plug V=3 into Euler's Pulchritudinous Formula? Or E=7?