## Archive for May 25, 2015

### Let Me Pencil You In

Pencils are infintely useful yet ridiculously simple — just a cylindrical piece of graphite surrounded by a hexagonal wooden sheath.

Well, typically.

Pencils come in all shapes and sizes, actually. They often have hexagonal cross sections, though some are octagonal, rectangular, circular, and oval.

Heck, there are even pentagonal pencils…

Which has to make you wonder, do we really need pencils in such a wide variety of shapes?

The answer may be no, but there is a practical reason for the multitude of cross sections. Can you think of any possible benefits that a rectangular pencil would have over a circular one, or vice versa?

The following problem about a pencil comes from Peter Winkler’s *Mathematical Mind-Benders*:

A pencil with pentagonal cross-section has a maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?

And here’s a good Fermi question:

How many pencils are there in the world?

I have no idea what the answer is, but one respondent to this question on www.answers.com said, “42,462,013,000,000,000 pencils about.” The amazing part is that **17 people found this useful**!

Slightly less ambiguous is this question:

How many pencils were used to make this sculpture by George Hart?

Or maybe you prefer selected-response items…

Which of the following is the best estimate for the length of a continuous line that could be drawn using a standard pencil?

- 0.35 mile
- 3.50 miles
- 35.0 miles
- 350 miles

Or maybe you’re tired of all these questions. You didn’t come here for a quiz. You came here for some jokes. Fine.

Did you hear about the constipated mathematician?

He worked it out with a pencil.What kind of pencil?

A #2 pencil, of course!What’s the largest pencil in the world?

Pennsylvania.

If you’d like to learn more about pencils and their history — and, let’s be honest, who wouldn’t — you can **download a free copy** of Every Pencil is a Sandwich. In return, you’ll be asked to sign up for the pencils.com newsletter. If you love pencils and use them as much as I do, receiving the newsletter will be a treat, not a burden!