Carolyn's Daily Posts: 2011

October 3, 2011

What Are Partition Numbers?



     The numbers game—not something I enjoy or look to read about. However, the title of an article, The New Math, not only intrigued me but increased my vocabulary by adding the phrase partition numbers.

     Partition numbers are the basis for adding and counting…they are a crazy sequence of integers which race rapidly off to infinity…  according to Emory University mathematician Ken Ono, is unveiling new theories that answer old mathematical questions. He and his research team have discovered that partition numbers behave like fractals—rough geometric shapes made up of repeating patterns that appear the same when viewed at any size or magnification.

     I recognize fractals—at least, I can sometimes identify them—because the online Jigzone puzzle site has a category labeled fractals. I enjoy putting those jigsaw puzzles together.

Online fractal design jigsaw puzzles are fun to do

     On the surface, partition numbers seem like mathematical child’s play. A partition of a number is a sequence of positive integers that add up to that number. For example, 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. So we say there are five partitions of the number four.

     It sounds simple, and yet the partition numbers grow at an incredible rate. The amount of partitions for the number ten is forty-two. For the number one hundred, the partitions explode to more than 190,000,000.

     This provocative sequence evokes wonder, and has long fascinated mathematicians The work of eighteenth-century mathematician Leonhard Euler led to the first recursive technique for computing the partition values of numbers. The method was slow, however, and impractical for large numbers. For the next 150 years, the method was only successfully implemented to compute the first 200 partition numbers.

     Until the breakthroughs by Ono’s team, no one was able to unlock the secret of the complex pattern underlying the rapid growth of partition numbers.

     Now I have a peek into a mathematical problem and the fresh theories reveal the ancient nature of numbers.

     Anything further will take much study, which I am not prepared to do. But the discussion is interesting, and I will view fractal jigsaw puzzles a little differently now.


The New Math:  Fresh theories reveal the ancient nature of numbers



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