Are marbles considered circles or spheres?
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Spheres, they’re three dimensional. Circles are two dimensional, FLAT.
Circles are 2 dimensional, spheres are 3 dimensional. Marbles are 3 dimensional. Ergo.
I’ve often wondered what a 4th dimensional marble would look like. I’ve seen models of 4th dimensional cubes (hypercubes), and that’s easier for me to understand. But 4th dimensional spheres are harder.
A sphere is just a circle that looks the same no matter where you position yourself around it. Imagine a circle on a very thin sheet of glass. You’re looking straight down at this flat piece of glass and you see a circle. Now, start to tilt the glass (you can use paper for convenience). The circle becomes more and more elliptical as the surface it’s drawn on tilts. Eventually, you are looking right at the edge of the sheet and the circle seems to have disappeared.
Now imagine a marble glued to the surface of the glass. No matter how you tilt the glass, it still looks like a circle. That’s a sphere.
To complicate things a bit, to a mathematician sphere only refers to the surface. Mathematically, a marble would be considered to be a ball. A basketball would be a better approximation of a sphere.
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