Just a geometry puzzle for you... I know the answers.

1.) What is the only 2 sided shape?

2.) what is the only shape with an infinite number of sides?

  1. any bidimentional shape has two sides
    top and bottom

  2. a sphere

Ecmandu has to define the word “side”.

You were damn close!

I know you won’t find my exact wording …

So I’ll give you the answer…

1.) a semi-circle
2.) a circle

What’s interesting about the second one is that the only shape that has infinite sides is the only shape that also has only one side.

I thought it might be fun for you to think about.

well it appears that you are using only two dimensions
i used three

Oh, you can go infinite dimensions… same principle applies. What’s a hyper sphere for example? Etc…

It’s about the concept first and foremost

Jamesian. :wink:

Ok smartasses. Side is what defines an indentation or protrusion (angle or arc).

And that’s why I said you should define the word “side”.

How is it that a circle has an infinite number of sides but a semi-circle only has two sides?

Which is a logical contradiction unless you’re using the word “side” to mean one thing in the first part of the sentence and another in the second part.

Doesn’t that imply sides are necessarily straight lines?

There are no straight lines in a circle.

The better term for these suggestions is “faces” rather than “sides”.
A “top” and “bottom” of any 2D shape would be its 2 faces, and critically - only when viewed in 3+ dimensions.
Any bi-dimensional shape viewed in 2 dimensions can’t show top and bottom faces, only any number of sides.
Many bi-dimensional shapes have more than two sides, and many have two - not just a semi-circle. Any lens shape has 2 sides, any shape that emerges from the overlap of two one-sided shapes like circles, but not restricted to circles, even a freakin’ heart-shape has 2 sides.

A sphere can be conceived as having either one curved face or infinite flat faces, but then so could any 3D shape with any number of vertices, and even with any number of edges so long as no edges connect with one another more than once.
Again, a sphere has to be viewed in 3+ dimensions here - it only really has sides when viewed in 2 dimensions, where it appears of course as just a circle, and the better term there is edges.

I dunno, Ecmandu, the word “only” in your original questions isn’t valid.

Two sided figures – Digons
infinite sided - Apeirogons

When I was conceiving this, I was thinking about reality, not ideal. If you have a perfect circle it’s only one sided, but… I know of no such circle when you magnify it… actually not even a line. Although (and this makes no sense to me), a line is defined as length without width. Technically, every line is a rectangle that doesn’t have perfect straight edges. (All lines have width in this sense.)

Each point of each edge is a fractal. Thus, every possible shape is infinite. And since you’re counting both sides of the circle, it’s somewhat of a cheat (the rectangleness of every line) the yes, that is two sided rather than one sided. Unless you define it as it’s perimeter.

So we take the micro… and see infinite sides at any point… we see the macro, we just see a point.

And that was my point. 1 from the perspective of thinking about the micro is: the only shape that has infinite sides is a dot from the macro as it’s perimeter.

Doesn’t that mean the answer to “2” is every single real shape?
And thereby the answer to “1” is there are no such shapes in reality?
So still the word “only” doesn’t apply to either question.

If you strictly only measure the perimeter without protrusions, inclines (deviation from a path or direction) or indentations (not microscopically), then a circle is the only 1 sided shape that contains infinite angles and 1 arc. If you have two indentations, inclines or protrusions (not microscopically), you have 2 angles etc… in the macro.

In the macro a circles perimeter only has 1 side…, however, in the macro, unlike other shapes, it is always protruding and extruding, and that’s what also defines angle. In something like a line (in the macro) there is zero protrusion and extrusion.

When it turns into a protrusion or extrusion by some type of non uniform bent, then it has demarcated angleness.

Again, that depends on how you define the word “side”. Depending on how you define it, perfect circles can be zero-sided, one-sided, two-sided and so on. So far, you have refused to provide a clear definition.

An angle is something that exists between two rays that share an end-point. And rays happen to be straight lines, don’t they? Given that circles have no straight lines, I would say that circles have no angles whatsoever (rather than an infinity of them.)

A circle (unlike any other shape) has the maximal number of rays.

But there are no rays in a circle.

Like I’ve tried to explain before when it comes to this particular shape: 0 = infinity.

There are no rays and there are an infinite number of rays.

  1. Infinity is a number greater than every integer.

  2. Zero is not greater than every integer (i.e. there are integers greater than zero e.g. number one.)

  3. Therefore, “zero” and “infinity” refer to two different concepts.

Two aspects of the same phenomenon…

Just like light: particle and wave.

0 is the same as 1: in one everything is exactly the same (which equals zero)