# Make A Flexagon for your Valentine

What better way to show your Valentine you care, than to make them a flexagon! You can print out this cool Valentine tri-tetraflexagon card, featuring teddy bears, at Aunt Annie’s Crafts. Or, you can choose the plain frame template and add your own pictures. But, if you want to make them for an entire class, make sure you start now! It takes some time to print, cut out, and fold. (My son is making these, and he has made enough for about a third of his class so far.)

If this seems like too much work, there are tons of cute math-themed pictures on the internet you can turn into Valentines. Last year, we found cute a Sierpinski Valentine.

# October is the Month of the Flexagon

A few years ago, recreational mathematician, Vi Hart, declared October “Fexagon Month” in honor of Martin Gardner. Gardner, born October 21, 1914, wrote a monthly column on “recreational mathematics” for Scientific American from 1965 to 1981, and it all began with his article on hexaflexagons in the December 1956 issue.

A flexagon is a flat model that can be flexed or folded to reveal faces besides the two that were originally on the front and back. Watch these two videos from Vi Hart to learn more about the history of flexagons and how they work:

Flexagons are very cool to make and fun to play with. You can try making your own hexaflexagon from a strip of paper like Vi Hart shows in her video, or you can go to one of the tons of websites with colorful, printable templates that you can print out and fold according to the directions. Here are just a few:

You can even make a flexagon template using your own photos using the tool here.

Happy Flexagoning!

# Pascal’s Triangle Patterns

Pascal’s triangle is a triangular array of the binomial coefficients. (But don’t worry, it isn’t important to understand binomial coefficients to do this activity.) Pascal’s Triangle is named after mathematician Blaise Pascal. Pascal did not invent this array, but he was the first to develop many of its uses and was the first to organize all the information about it together in a treatise.

To create your own Pascal’s Triangle, place a 1 in the first row (which contains only 1 number). In subsequent rows, each number is the sum of the two numbers above it, treating space outside the triangle as zero. Therefore, the next row, contains 0+1 or 1 and 1+0 or 1. The next row is 0+1, 1+1, and 1+0, as shown in the animation below.

The cool thing about Pascal’s Triangle is that there are a ton of patterns you can find. Here are just a few:

1. The first diagonal is all ones.
2. The second diagonal is the counting numbers.
3. The third diagonal is the triangular numbers.
4. The horizontal sums (adding across a row) are the powers of 2 (20=1, 21=2, 22=4, 23=8, 24=16, etc.).
5. Each row is a power of 11 (110=1, 111=11, 112=121, 113=1331, etc.).
6. And my favorite of all: if you color the odd numbers one color and the even numbers another color, you get a pattern that looks like the Sierpinski Triangle fractal.

Can you find any other patterns?

For more patterns, check out this cool page at Math is Fun. If you would like to challenge your kids or students to fill in Pascal’s Triangle and find some of the patterns, I have a worksheet here.

# How to Fall in Love with Math

Manil Suri, a mathematics professor at the University of Maryland, had a great op-ed in the New York Times this past weekend called How to Fall in Love with Math. Suri argues that even those of us without advanced knowledge of math can appreciate its power and beauty. He writes:

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

# Math: What is it good for?

A new school year has begun, and soon I will have a new group of after-school math club students. At the first session, I always like to just talk to the kids about why math is important, in terms of future careers, as well as, in everyday life. After all, few are going to grow up to be mathematicians, so why do they need all this math anyway?

I start by asking them to think of ways they or the grown-ups in their family use math:

• Dividing something to share,
• Dealing with money – shopping, tipping, budgeting
• Art and craft projects (measuring, buying the right amount of supplies),
• Home improvement projects,
• Time management

Next, we think about some of the careers that use math:

• Scientists and engineers
• Computer programmers
• Medical professionals (doctors, nurses, technicians),
• Designers
• Contractors and landscapers
• Bankers, accountants, and other finance professionals
• Anyone who owns a business – budgets and accounting

This year, I plan to also show them how math is important in lots of fields and shows up often in scientific articles. Here are just a few recent headlines:

In the past, I have finished off the lesson, by showing this video about designing the Mars Curiosity Lander. Lots of math and WAY COOL!

This year, I plan to show this great video about why math is cool and interesting and important for many kinds of careers.