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Paenza’s problem is an example of

##### Paenza observes, “With every fold we make, the paper doubles in thickness from the previous value.” How would you express this using mathematical notation?

Paenza’s problem assumes which of the following:

##### Paenza says, “Folding a piece of Bible paper 45 times, we get to the moon. And if we double it one more time, we get back to Earth.” Does this surprise you? Why or why not? Does it make the great distance between the Earth and the moon any more comprehensible? What other expressions have you heard that help you get a good sense of scale and distance (like the distance from the Earth to the moon)?

If we fold the paper ten times, how thick would it be?

##### Do you enjoy working on problems like the one that Paenza poses in this lesson? Why or why not?

After how many folds would the paper be as tall as the Empire State Building?

Paenza asks how thick the paper would be after 30 folds, and the answer is

Additional Resources for you to Explore

The exponential growth that Paenza plays with is hypothetical, but real-world exponential growth patterns exist all around us—in microbiology, economics, public health, and technology, to name just a few. Identify some instances of exponential growth in one or more of these domains. Working with classmates, create an exhibit for younger students that defines exponential growth, shares real-world examples, and suggests simple experiments that they can do in order to see exponential growth in action.

Assume that you’re working with a piece of paper that’s 0.001 cm thick, as Paenza proposes, and one meter on each side. At what point will you be unable to fold the paper anymore because its thickness has exceeded the area available for folding?

Adriàn Paenza: Matematica, Estas Ahi? http://www.epubbud.com/book.php?g=JYQ2E5DP

YouTube: IBM’s Mathematics Peepshow: Legend of the Chessboard http://www.youtube.com/watch?v=t3d0Y-JpRRg

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