Something to Try
This surprised the heck out of me! Please describe your experiences with this in the comments. It sounds a bit complicated but you can do the whole thing in 15 minutes.
Find a full-length mirror, a friend, some tape, and some string. You can do without the string if necessary. Don't try this in a slanted room - the wall and floor should be as perpendicular as possible. The mirror need not touch the floor, however.
Stand back from the mirror a distance equal to your height. Imagine a rectangle surrounding your body so that you just fit - the top of the rectangle touches the top of your head, the sides of the rectangle touch the sides of your body at your widest part (shoulders, for most people), the bottom of the rectangle touches the bottom of your feet.
Your image in the mirror as you see it could also be surrounded by a rectangle as described above. Will the rectangle around your mirror image be larger than, smaller than, or the same size as the rectangle around your real-life body? Make a prediction.
Now, have your friend use segments of tape and/or string to mark off the rectangle around your image in the mirror so that your image just fits within the rectangle. Compare it's size to the size of the imaginary rectangle around your body. (You can use pieces of string to compare, or measuring tape, or just eyeball it).
How does the rectangle in the mirror compare to the rectangle around your real-life body? Was your hypothesis correct?
Predict what would happen to the size of your image in the mirror if you moved closer to the mirror or farther away from it. Would your image fit in a larger or smaller or same-sized rectangle? Try it!
Can you explain what happens using geometry?
Those of you with compact mirrors in your purses can play around with those as well. This is a good option for people who wear a lot of make up but have no friends. ;-) Does it make a difference how far you hold the compact from your face?
Find a full-length mirror, a friend, some tape, and some string. You can do without the string if necessary. Don't try this in a slanted room - the wall and floor should be as perpendicular as possible. The mirror need not touch the floor, however.
Stand back from the mirror a distance equal to your height. Imagine a rectangle surrounding your body so that you just fit - the top of the rectangle touches the top of your head, the sides of the rectangle touch the sides of your body at your widest part (shoulders, for most people), the bottom of the rectangle touches the bottom of your feet.
Your image in the mirror as you see it could also be surrounded by a rectangle as described above. Will the rectangle around your mirror image be larger than, smaller than, or the same size as the rectangle around your real-life body? Make a prediction.
Now, have your friend use segments of tape and/or string to mark off the rectangle around your image in the mirror so that your image just fits within the rectangle. Compare it's size to the size of the imaginary rectangle around your body. (You can use pieces of string to compare, or measuring tape, or just eyeball it).
How does the rectangle in the mirror compare to the rectangle around your real-life body? Was your hypothesis correct?
Predict what would happen to the size of your image in the mirror if you moved closer to the mirror or farther away from it. Would your image fit in a larger or smaller or same-sized rectangle? Try it!
Can you explain what happens using geometry?
Those of you with compact mirrors in your purses can play around with those as well. This is a good option for people who wear a lot of make up but have no friends. ;-) Does it make a difference how far you hold the compact from your face?
posted by ms. v. at 5:16 PM
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