Sunday, May 18, 2014

Nature, History, Explanation, and Doing of Math

Al-Khwarizmi made this week's post really easy (although time consuming) due to the rich contributions of his work.  This brilliant mathematician allows me to touch upon a little of everything for this course -
  • Explaining math (the origin of our number system)
  • The Nature of Mathematics (linking geometry and algebra)
  • The History of Mathematics (the role al-Khwarizmi played at the House of Wisdom)
  • Doing Math (creating a tiling inspired by the Islamic tilings)
This is so cool! I found this image as I was researching our most recent mathematician, al-Khwarizmi.  While the image is what caught my eye, as I dug deeper, I found out that al-Khwarizmi actually invented our numeral system by determining the number of angles formed by line segments. This is one of the most basic representations of how algebra and geometry are linked.  Rather than being English numbers, these are actually considered to be Hindu-Arabic numbers. 
Al-Khwarizmi is known as the Father of Algebra.  At the end of the forward for his book, the Compendious Book on Calculation by Completion and Balancing, al-Khwarizmi gives credit to God for encouraging him to persevere through difficult times to ultimately write such a concise and useful work of mathematics.  The word "algebra" is a Latin derivative the Arabic word Al-jabr, which came from his Compendious Book.  Attached is a link to a short and easy to follow description of what algebra means: The Origin of the Word Algebra  .

We can find further evidence of Al-Khwarizmi linking algebra and geometry through his use of geometric shapes (squares and units) to create algebraic expressions, as we saw when using algebra tiles in class on Thursday.  Here is an example of a problem I did using the virtual algebra link  Virtual Algebra tiles provided in class:

As one of the original contributors to the the House of Wisdom (a library, translation establishment, and school in Baghdad, Iraq established in the 700's), al-Khwarizmi is known as one of the most famous mathematicians at the House of Wisdom.

Inspired by the Islamic Tilings, I tried to create a tessellation with the letter K.  Seeing that could be rather challenging, I decided to think of letters or numbers that might fit easily together.  The number 4 came to mind.  Since my daughter is involved in 4-H, I thought I might be able to use that combination of numbers and letters for a tiling.  My original attempt at this tiling failed because the stem of the 4 was not long enough to allow for the tiling as I was picturing it.  When I extended the stem of the 4 - "Eureka!" (oh, wrong mathematician - Archimedes said that!), it worked!  I was able to tile in the H along side of the 4, separated by a hyphen (light blue square).   Here is the tiling I created:

After exploring al-Khwarizmi on my own, he became very interesting and inspirational to me.  I saw the depth of his workings in so many facets of math:  history, nature, communicating, and doing math.  Prior to being introduced to this brilliant man in my math capstone class, I had not realized that Islamic mathematicians had such a profound impact on math as we know it today.  Al-Khwarizmi sparked my interest in math history, a subject I have usually steered clear of.  I thought, if this guy is so interesting, and his math ideas are so engaging, then there must be other mathematicians who are also intriguing and fascinating.   Al-Khwarizmi is the reason I decided to do my semester project about the great mathematicians throughout history.  Math history anyone?


  1. Kind of potpourri post - like it.
    clear, coherent, complete, content: +
    consolidated: Think about how to summarize. One framework to use to summarize is answer one or more of: what? (important bits) so what? (why important) or now what? (what's next).

  2. The image of the numbers is very interesting. It's weird to think that if this was done on purpose or if this was simply a coincidence. Sort of like the chicken and the egg; which came first, the look of the numbers or the idea of the number of angles in them.
    I also really liked how you incorporated your own life into math, figuring out a way to tessellate 4-H. Turned out pretty cool.