The objective of this article is to cause you to use several different parts of your brain's faculties from both hemispheres. The exercise is truly (and legally!) mind-expanding. I was always Leery of Timothy -- But was Timothy Leary of me?
Solutions To Our Last Post, Where I'll Give You Answers Without Explanations - PERCEPTION EXERCISES:
1) Which of the two figures is more stable, standing on its widest surface (on either end -- you choose)? The Cone. It might have something to do with the width of the base versus the "width" (merely a point) at the top.
2) How many cones could you fit (with the dimensions in Figure B) or could you insert into a cylinder (using the same dimensions as in Figure B)? Only one. Despite the fact that a cone contains only one-third of the volume of a cylinder, the size of the base is the limiting factor. Bet you thought the answer was two... well then, don't ever bag my groceries at the supermarket.
3) If you roll a cylinder across a table top, what type of shape would it create? A large circle, the radius of which would be equal to the height of the cone. Close your eyes and you'll see it more clearly (this is not an oxymoron)
4) If you push a cylinder (by its wide side) on a table top, what kind of a shape would it create? It would create a long rectangle, until it finally rolled off the table top. We call this the "Toilet Paper Effect" (No. We actually don't. But It's hard to know if that statement is true because I am a pathological liar)
5) If you could glue a limitless number of same-sized cones together at their respective tips, what type of geometric solid would this fusion resemble from the outside? A sphere, with the complexion of a golf ball.
6) If you knocked both a cone and a cylinder over, which of the two shapes is more likely to stay closer to you (instead of rolling under the couch where the dog might accidentally eat it?)? The cone. Just try to imagine a puppy rolling a cone across the room; not picture the same puppy with a soup can or a toilet paper tube.
7) Assume that the widest end (or at least one end) of each of the shapes were open, which could you stack that would require less space? The cone. Just take a walk over to the office water cooler and look at it. Go on. Cone-shaped cups are stackable. Even truncated cone-shaped cups are stackable. Cylinders have to be stored side by side -- although that can be done in a number of ways, one of which would create a shape which, if looked at head-on, would be shaped like a pyramid... or like....a cone!
8) If both shapes were filled with Styrofoam (or even vermiculite... choose any filling that you wish, as if you were at Aunt B's Yogurt And Cupcake shop) which one would float on its side, and which one would bob? The cone would bob, and the cylinder would merrily spin on its side.
9) Why do you think that cones are used for automobile steering system precision testing, while cylinders are selected to be filled with sand to buttress certain highways (near toll booths and such) in the event of a car crashing into them? Because although the base size is still the same and the cone might actually be more stable, you can fill the cylinder with three times as much buffering material to absorb the impact of the car driven by the imbecile who was texting. Just an example. The Braintenance Blog does not preach. It couldn't anyway -- it does not have the power to speak -- it is inanimate.
10) Bonus! You get to reduce three dimensions to two! Position both shapes to be standing upright, and side-by-side. Cut each in half with a laser beam (or a sword, if you'd like). Without touching the bottoms, throw the tops away. Looking at each of the halved shapes at eye-level, which one will look like a rectangle, and which will look like a trapezoid? Saw a cylinder, get a rectangle if seen from the front; saw a cone, get a trapezoid if seen from the front.
NOTE: In actuality, if you looked at each in the full three dimensions, the cylinder would still be a cylinder (just shorter and stumpier), but the cone would have become a frustum.
- 2, 4, 8, 16, 32, ?
- 0, 1, 1, 2, 3, 5, ?
- A, C, E, B, D, F, C, E, G, D, F ?