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!

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/2011/11/02/test-yourself-math-nov-2-2011-2/

This article is about the $18 million reportedly earned by Kim Kardashian and Kris Humphries as a result of their 72-day marriage.

How many years would an average person have to work in order to earn that much?

Polygonal Oddities

This is a crazy collection and categorization of mathematical oddities.

http://www.recmath.org/PolyCur/p6odd/index.html

Here, the word oddity has a specific, technical mathematical meaning:  an oddity is a figure with at least one line of symmetry that is made up of an odd number of copies of some polygon.

I’ve never heard of oddities before, and I learned a lot of new vocabulary words while exploring this page:  polyform, hexapent, and quinquerotary, to name a few!

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