# "Sphere ---> Circle, Ball---> ?"

I am struggling with a puzzle in Swedish. I will translate it to English:

1. Sphere ---> Circle, Ball--->?
• a) Sphere
• b) Ring
• c) Circle
• d) ?

The answer provided is "It is hottest that Ring is correct based on a 3D/2D perspective or if you convert the objects into other alternatives to things that are "handled" with similar geometric shapes..."

To give a bit more context, the puzzle is asking for the word that can replace "Ball" in the same way that "Circle" replaces "Sphere". The possible answers are "Sphere", "Ring", "Circle", and an unknown option.

I have been trying to solve this puzzle, but I'm not sure where to start. I have considered the different geometric properties of the shapes and their relationships, but I can't seem to find a clear answer.

Here is where I found the puzzle: https://cdn.discordapp.com/attachments/869145673197580298/1083855309942030346/PIL_-_sammanfattning_av_fragor_oscar_bakhouch.doc

• A ring could be considered a generalisation of a circle. It also could’ve been a mistranslation because ‘It is hottest that (this)’ does not make sense in English. Commented Mar 11, 2023 at 16:58
• What do you mean by the first statement? Commented Mar 11, 2023 at 17:57
• Sphere and circle are mathematical concepts. A Ball is a physical object that has the shape of a sphere. So the answer would be a physical object that has the shape of a circle, that is a ring. Commented Mar 11, 2023 at 19:35
• @FlorianF Ball is also a mathematical object, namely the interior of a sphere. A sphere is the surface of a ball. The answer would then be disc, which is the interior of a circle. Commented Mar 11, 2023 at 23:37
• @jarmanso7 Jaap is correct. In higher math, for example real analysis, "circle" refers to the boundary and "disk" refers to the interior. Commented Mar 12, 2023 at 6:44

"Disk/Disc"? https://en.wikipedia.org/wiki/Disk_(mathematics)

Because:

Sphere is the shell, like Circle. Ball is the volume surrounded by a Sphere, and Disc is the area surrounded by a Circle?

As someone studying topology, though I might be overthinking this, I would say the answer is:

Two spheres conjoined by a point.

The action done to the shapes might be:

To exclude two points and get an absolute retract of the resulting space.

Though, this explanation assumes that:

The ball is an open ball. That means, the ball has its boundary excluded.

If this is really the answer, we can speculate what would happen to other shapes as well. For example:

A torus would become the wedge of three circles.

I think the answer is based on:

Cross Section

If you:

Cut a solid sphere in half, the cross section will be a circle.

However, if you:

Cut a hollow ball in half, and the cross section will be a ring. (ball doesn't necessarily mean hollow in english, but it could be a translation issue)

• "Cut a hollow ball in half, and the cross section will be a ring." Could you elaborate why? I can't picture it in my head. Commented Mar 14, 2023 at 5:51
• Yes, this makes sense but assumes significant translation issues - that the word translated "sphere" actually means "ball" and vice versa, that the word translated "circle" actually means "disc", and that the word translated "ring" actually means "circle". Commented Apr 14, 2023 at 8:44
• I mean, the answer can be anything you want if you give "sphere", "circle", "ball" and "ring" colloquial, non-rigorous, and arbitrary definitions. Mathematically, spheres aren't solid, circles aren't filled, balls aren't hollow, and rings aren't two-dimensional. Commented Apr 14, 2023 at 15:53