Proportional Reasoning-1
Why some pictures look stretched
Find out why some stretched pictures of a tiger look wrong and others look right.
Everyone resizes pictures on a phone or computer. Sometimes the result looks fine, and sometimes it comes out stretched or squashed. Why?
The book shows five pictures of a tiger:
| Image | Width | Height | Looks |
|---|---|---|---|
| A | 60 mm | 40 mm | right |
| B | 40 mm | 20 mm | stretched |
| C | 30 mm | 20 mm | right |
| D | 90 mm | 60 mm | right |
| E | 60 mm | 60 mm | squashed, fatter |
A, C and D look right even though they're quite different sizes.
The obvious guess is the shape of the frame: E is a square, after all. But B is a rectangle like the others and still looks wrong. So something else is going on.
Compare A with C. The width goes from 60 to 30: half. The height goes from 40 to 20: also half. Both have changed by the same factor, ½. The picture looks right.
Now compare A with B. The width goes from 60 to 40, a drop of 20 mm. The height goes from 40 to 20, also a drop of 20 mm. The same difference in both, and the picture looks wrong.
Check the factors instead. The height halved: 40 to 20. But the width didn't: 60 to 40 is two-thirds, not a half. The two dimensions changed by different factors, so the tiger stretched.
That's the whole idea, and it's worth saying carefully: what keeps a shape looking right is the same multiplying factor, not the same amount added or taken away. When two quantities change by the same factor, we say the changes are proportional. (Check D for yourself: 90 is 60 × 1½, and 60 is 40 × 1½.)
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