Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

https://learning.blogs.nytimes.com/2011/11/21/test-yourself-math-nov-21-2011/

This problem is related to the number of U.S. college students graduating with degrees in engineering.  How many of these graduates are women?

Math Photo: Anamorphic Art

At the Bridges Math and Art Conference, I was exposed to a wealth of fascinating mathematical and artistic ideas, like these anamorphic images by Jan W. Marcus.

The challenge for the artist is to produce an image on a flat surface that will appear rectangular when viewed on the surface of the cylinder.  My mind swirls with thoughts of vector projections and polar coordinates when I view these images.

Not to be outdone, Francesco De Comite created a three-dimensional curved sculpture that projects to a polyhedron on the surface of a sphere!

Graphing the Collatz Conjecture

This a beautiful representation of the infamous Collatz Conjecture:

http://www.jasondavies.com/collatz-graph/

The Collatz conjecture is one of the great unsolved mathematical puzzles of our time, and this is a wonderful, dynamic representation of its essential nature.

One compelling aspect of the Collatz conjecture is that it’s so easy to understand and play around with.   Start by choosing any positive integer, and then apply the following steps.

Step 1)  If the number is even, cut it in half; if the number is odd, multiply it by 3 and add 1

Step 2)  Take your new number and repeat Step 1.

For example, starting with 10 yields the sequence

10 \longrightarrow 5 \longrightarrow 16 \longrightarrow 8 \longrightarrow 4 \longrightarrow 2 \longrightarrow 1 \longrightarrow 4 \longrightarrow 2 \longrightarrow 1 \longrightarrow ...

The Collatz conjecture simply hypothesizes that no matter what number you start with, you’ll always end up in the 4 \longrightarrow 2 \longrightarrow 1 loop.

Have fun!

2011 Sloan Award Winners

I would like to extend my congratulations to the recipients of the 2011Sloan Awards for Excellence in Teaching Science and Mathematics.

These awards, presented by the Fund for the City of New York, recognize outstanding teachers in the New York City Public School System.  I am very proud to have received this award in 2010.

As a teacher, the current public discourse that focuses mainly on what is “broken” in public education can be deflating.  It is wonderful to be a part of something that honors the great work teachers do every day.

Here’s a short write-up in the New York Times about the winners, and bios and videos of this year’s recipients can be found here:  http://www.fcny.org/fcny/core/sae/.

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