Out for a bike ride, I noticed this naturally occurring tree diagram.
A few days later, the lovely red leaves were gone.
Application Technology
4.74 Degrees of Separation
This story in the New York Times summarizes a recently published study about interconnectedness on Facebook.
A computational analysis of the 721 million worldwide Facebook users shows that the average distance between two people is about 4.74 “friends”. Roughly speaking, given anyone in the world on Facebook, a friend of your friend is likely to be friends with a friend of their friend.
An amazing result! And a cool application of graph and network theory. Now the questions becomes “What can we do with this knowledge?”
Challenge NYT
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?
Art Photography Uncategorized
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!
Challenge Representation
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
The Collatz conjecture simply hypothesizes that no matter what number you start with, you’ll always end up in the 
Have fun!