## Posts tagged ‘pentagon’

### 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?

1. 0.35 mile
2. 3.50 miles
3. 35.0 miles
4. 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!

### Math Dot-to-Dot

Connect-the-dots puzzles usually aren’t very interesting. The purpose of these puzzles is to teach kids the counting numbers, or the alphabet, or something else that occurs in a particular order. Consequently, a dot-to-dot puzzle often contains an image that can be identified before the dots are connected, and the image then serves as a scaffold to help students learn the items to be ordered. For adults who know how to count and can identify the image immediately, what’s the point?

For instance, can you identify the shape that will be formed by this connect-the-dots puzzle?

If you had trouble with that, you may want to stop here.

Connect-the-dots puzzles without numbers, however, can yield interesting results. For instance, if the numbers and segment are removed from the puzzle above, the dots can be connected to form more whimsical shapes. With a little creativity, it can result in a fun picture.

So, here’s the challenge I now pose to you:

Using either set of dots below, connect them in any way you like. Allow lines to cross one another, use curves, use only some of the dots, whatever. Be creative.

Then upload your image(s) to Math Dots on Flickr, or post them in the comments below.

Option 1:

Option 2:

### Pentagon Flower and Polygonal Jokes

Frisbee golf is a sport enjoyed by many mathy folks. Almost certainly, this is a result of the physics that surround the flight of the disk.

When a ball dreams, it dreams it’s a Frisbee.
— Stancil Johnson

I love Frisbee golf, because I can make the Frisbee bend and curve around trees in a way that I’m not able to do with a real golf ball. But I also love it because Frisbee golf courses are typically located in beautiful natural settings, like my home course at Bluemont Park in Arlington, VA, which meanders through an urban park with trees, flowers, and a creek.

While playing a round with my sons yesterday, I encountered some flowers with five‑fold rotational symmetry. Taken by the perfect pentagonal shape in the middle of the flower, I snapped a pic to share with you:

Speaking of closed plane figures bounded by straight sides, here are pieces of some recently overheard conversations at the Icosagon Cafe:

• “He’s degenerate, but I say, ‘Let digons be digons!'”
• “I don’t have the energy for another attempt. Trigon.”
• “That hot chick walked away. Pentagon.” (Warning: OFFENSIVE; see definition 2 of pent in the Urban Dictionary. )
• “I took an antidote for the wizard’s curse. Hexagon.”
• “I just looked at the calendar. Septagon. Octagon. Nov is here!”
• “Nonagon. They’re all here!”
• “Someone stole my pack of cards. Decagon.”
• “My parrot just died. Polygon.”

Just outside the cafe, a hendecagon was walking by…

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

## MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.