Pinscreen Approximations

I’ve always enjoyed playing around with pinscreens, but only recently did I realize what cool mathematical concepts they display!

Pinscreen Approximation

For example, the image above shows an approximation of the volume of a hemisphere using right cylinders.  A pinscreen Riemann sum!

And the images below suggest how we might approximate the areas of a circle and a square using pinscreens.

pinscreen circle

pinscreen square

Compute the ratio of raised pins to total pins, and multiply by the total area of the pinscreen.  A pinscreen Monte Carlo method!

Any other cool math hiding in there?

 

 

02/15/2015 — Happy Permutation Day!

Today we celebrate the second Permutation Day of the year!  I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.

02152015

Additionally, today is a transposition day, as a single swap of two digits is all that’s need to turn the day-month into the year.

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today.  Just remember, for some operations, order definitely matters!

Exploring Compound Interest

Go to a <a href="http://bucks.blogs.nytimes.com/2013/01/07/investing-money-plus-lots-of-time-equals-excitement/">related post</a> about a topic one blogger calls “incredibly important to share with your kids.” »My latest piece for the New York Times Learning Network is a math lesson exploring personal savings and the power of compound interest.  The piece was inspired by a new program in Illinois that creates an automatic payroll-deduction savings program for all state residents.

In addition to exploring the basic ideas of savings and compounding, students are invited to analyze the merits of this state-run program.

The automatic retirement savings program mentioned in the article is described as a zero-fiscal-cost program because it does not require any government funding to run. This is because the savers themselves pay the costs, in the form of fees to financial institutions, amounting to 0.75 percent of their total savings each year.

Have students compute the costs associated with maintaining the account for each of the typical savers they profiled in the previous activity. One way to do this is to compute 0.75 percent of the total value of the savings account each year, before interest is computed. This is an estimate of the amount that would be paid in fees that year, and thus should be subtracted from the amount in savings.

The entire piece is freely available here.  Hopefully students will get a sense of the power and value of long-term savings, and maybe ask a few good questions about the the true price of zero-fiscal-cost programs.

Math Photo: Surprising Heptagon

Surprising Septagon

It took several hundred encounters with this park bench before I realized it was a heptagon!  I don’t see many regular, seven-sided figures in my experience, which made this a surprising discovery.  I wonder what prompted this design choice.

Septagon Angle

Like most real-world instances of perfect geometric objects, it doesn’t exactly measure up.  But what’s a few degrees between n-gons?

 

 

 

New York State Master Teacher Program

NYSMTPI’m happy to announce that I am now officially a member of the New York State Master Teacher Program.

The NYSMTP is designed to connect great math and science teachers from around New York State through networking, professional development, and professional service.  The program is inspired, in part, by the Math for America Master Teacher program in New York City, which I have been actively involved in for the past 9 years.

This past summer I was fortunate to attend a NYSMTP retreat in upstate New York, and I had a fantastic time.  I talked with teachers from all over the state, and learned a great deal about the many different, and similar, things going on across New York.  I also ran a workshop on using Twitter for professional development, which I think is a natural medium for connecting teachers in a program like this.

I’m looking forward to working more with great colleagues from across New York State!

 

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