Saturday, September 1, 2012

it IS beautiful!

"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."  J.H.Poincare (1854-1912)

I've always enjoyed math as far back as I can remember.  I was good in math in school.  I remember other students wanting my help ... wanting my homework!  I also remember in 8th grade wanting to take Algebra 1 and my first year of a foreign language.  I requested to take both but I was told that I could not ... I was allowed to take the foreign language but not the algebra.  (I remember that incident as gender bias.)

Even though I enjoyed math as a student, I didn't see the beauty of math until much later.  As I began to attend math conferences as a teacher, I heard people talk about patterns, connections, references in math that to the best of my knowledge I wasn't taught in school.  It was in learning about the patterns and connections that I determined to share the beauty of math with my students.

One of my favorite exercises is exploring the patterns in Pascal's Triangle.  With elementary students we explore even and odd numbers - coloring them in - discovering the pattern of Sierpinski triangles.  In middle school we look at the patterns of polygonal numbers - square numbers, triangular numbers - and look for others in Pascal's Triangle.  In high school, the connection between the binomial theorem and Pascal's Triangle are noted.  At various levels we explore the connection between Fibonacci's Sequence and the Triangle ... with the challenge to discover other hidden beauty!

A favorite author I use as a resource to learn more about the beauty of mathematics is Theoni Pappas.  She has written numerous books, some of which I own, and I find her books accessible at all levels of learning.  One book I like to keep near my desk is her compendium of mathematical quotations.  I know that you can find hundreds online in the blink of an eye ... but there is something special about having a small volume of pertinent quotes on your desk!

I love to share quotes about the beauty of math with students because for so many students, math is painful and sometimes while learning the language and processes of math they miss out on the beauty!

"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics. " G. H. Hardy (1877 - 1947)


  1. I personally love these quotes as well. This is an interesting book that I read a while back:

    Thanks for sharing this!

  2. instillnessthedancingSeptember 1, 2012 at 4:01 PM

    Thanks for suggesting the book ... I'll check it out soon!

  3. @Jim Pai: Stop following me, Jim! O wait, I'm following you! We must share good taste in blogs. :))

    First, I LOVE your blog name and the heading above. So serene. And I'll have to check out what you're reading later. "I remember that incident as gender bias." Hard to imagine there was any other reason. That was terrible!! I couldn't agree more with the quote because math is so beautiful and elegant. But like you, I didn't see the beauty of math until I was out of college and taking visual math and seeing patterns. (I posted about first lessons in algebra and it was mainly all on patterns!) Funny, I was just at a post where I shared in the comments that I keep a Word doc of math quotes on my desktop. Your Theoni Pappas' book is much more beautiful, of course. To touch the pages of a book is something no Kindle-type tablet is going to replace.

    Thank you for this post, Beth, and I'm proud to feature yours on my blog at

    Happy blogging! Fawn

  4. instillnessthedancingSeptember 6, 2012 at 2:22 PM

    Fawn - thank you for your sweet post and for featuring my blog!

  5. Hi, Beth,

    I came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we're putting together. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter -- bringing math to children in an innovative, adventurous way. I’d really appreciate your help in getting the word out about the project.

    I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We're teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

    I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.
    Our concept is to create an exciting, web-based TV show that’s both fun and educational.

    If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you'd be interested in link exchanging (either on The Number Hunter site, which is in development, or on which is a well-established site with 300,000 page views a month) please shoot me an email. We're also always looking for input and ideas from other math educators!

    Thanks in advance for your help,


    1. Stephanie -

      I will post about the project in a blog - be delighted to do so. And definitely - I am interested in link exchanging.