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I shined my flashlight on a wall in terror. It was 2 in the morning at my place and I thought I heard a voice in my head. At first when I saw what was in my light, I jumped back because it looked monstrous. Then I realized that there was no true monster and I was probably hearing things such as the wind. But I did see 4 shapes.

The first shape seemed really natural and common.

The second shape seemed sort of like the first one, though some differences were there. We go in this shape more than you think.

The third one fit ironically three descriptions.

The fourth one is the third one stretched. I was estranged that there was only one curve, not two.

So I ask you, what is the relation between these four shapes? Maybe it will help to identify the shapes first.

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  • $\begingroup$ So, after 2 months I am back. I've been caught up with classes a lot, but I'll try to sick around from now on. These puzzles with horror, whether it comes from the presences of monsters, or just the setting, will be most of what I dish out, since it helps me provide a better setting in my opinion. $\endgroup$ – Xavier Stanton Nov 5 '18 at 0:54
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Maybe you were seeing

the conics?

That would be because

when you shine a flashlight on a wall, the wall "slices" the light cone, creating different patterns depending on the angle of the flashlight

The first shape seemed really natural and common.

When you shine a light on a wall, you'll usually see an ellipse. Ellipses are very natural; any inverse-square-law attractive force, for example gravity, can keep stuff in an ellipse shaped orbit.

The second shape seemed sort of like the first one, though some differences were there. We go in this shape more than you think.

When you shine the light straight at the wall, the light's shape is a circle. When we make no progress even with great effort, we go around in circles.

The third one fit ironically three descriptions.

that's probably a parabola, which you get by pointing the light so that the cone's outer edge is parallel with the wall. (still working on the extra clue part)

The fourth one is the third one stretched. I was estranged that there was only one curve, not two.

when you shine the light parallel with the wall, the light pattern is a hyperbola, which looks like a stretched parabola. A hyperbola usually has two parts, one in either direction, but since your flashlight only projects light forward, you only get one half of the double cone that is usually used to create the conic section.

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