I have emphasized over and over again to my Geometry students that "eyeballing" is never an acceptable justification for any argument. Today, I tried to make my stand a bit more compelling by presenting a series of optical illusions, a move to point out how unreliable our perceptions may be. Two lines that look congruent may actually be different lengths, or vice versa. An angle that looks like a right angle may not measure 90 degrees at all. Is that quadrilateral really a square? "Well, it looks like it is!" they tell me, exasperated with my unwavering prompts of "But do you know for sure?"
The reality is that our eyes and the sense that our brains try to impose on the world around us are completely unreliable. How we interpret the world may not be an accurate representation of the world. Or rather, what we "see" is simply that -- a representation. The images presented here are just two of a series of optical illusions I showed to my students, though these two most closely address the types of incorrect assumptions they might make with their work.
Ironically enough, students are allowed to make the assumption that a line is straight. Yet the following illusion suggests that even with straight lines, what we see is not actually truth.
Are the two red lines in the middle straight or curved?
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