In chemistry, we’re learning about molecular geometry which is a subject that takes a bit of visualization to understand. My teacher mentioned that girls tend to have poorer spatial reasoning skills, maybe because we are less likely to play with blocks and other similar toys as children. (He was probably citing this study). A few of the boys in my class were getting a little too cocky so I gave them this tough orthogonal projection problem to think about. After that they definitely realized that a slight tendency one way or another doesn’t mean much for individual cases or skill levels.
Anyways, just a fun little problem that tests your sense of spatial reasoning. Usually people think about it for a wile, get stuck, declare that it’s impossible, then figure it out in a flash of insight.
The goal is to draw the 3-dimensional (isometric) shape that matches the orthogonal projections:
First, an example.
Orthogonal Projections:
Isometric Solution:
Hopefully you were able to understand the drawings and figure out the solution!
Now for the tricky problem:
And before you feel too clever for having thought (like I did) of this:
Know that for the purposes of this problem, holes in the figure are represented in the engineering drawings by dotted lines. So the top and side views for the above would be:
Since there are no dotted lines in the initial two drawings, this is not the correct solution.
Think about it for a while and then, once you think you’ve solved it, scroll down for the answer. Remember, only one side view is provided so not every side has to look the same.
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Solution(s):
These are the two (similar) solutions that I have found (if you find another feel free to email me and I’ll update this post). The real jump most people have to make in finding the solution is to get away from thinking of the object as a cube. Once they realize that a slanted surface can serve as both a top and side view, they typically stumble on the solution pretty quick.