Feline Calculus for Everyone

Eadward Muybridge (1830 – 1904) was a British photographer who did several studies of animals and humans in motion. He set up a bank of cameras with fast shutters that would take pictures of the subject while it moved in front of them. The result is a series of stop-motion frames that allowed him to analyze the gaits of horses, cats, dogs, and other animals.

To introduce the concept of instantaneous velocity, my students look at Muybridge’s frames of a cat breaking into a run:

The background is divided into 5 cm blocks, so they can count the distance the cat covers over the frames. Each frame represents 0.031 elapsed seconds, so they know the total time the cat is moving. By looking at two or three consecutive frames, they can even estimate the instantaneous velocity of the cat at that time by calculating a difference quotient!

What I like about this is the fact that even Algebra I students could work through it and still get a nice understanding of the distinction between average and instantaneous velocity.

I learned about this activity from a presentation by Dr. Nell Rayburn, Professor and Chair of Mathematics at Austin Peay State University. Here are her original documents: Cat PhotosMuybridge Cat WorksheetMuybridge Cat Key.

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