Monday, October 12, 2015

The Fibonacci Sequence from 1202 and a Mathematical Art Project

When I was in college I took a great math class for elementary education teachers called Informal Geometry. It has come to mind recently in my search to help my daughter with her spatial reasoning skills for vision therapy. I spent quite a bit of time researching topics from our class, which led to new finds such as the Fibonacci Sequence...which led to quilt designs!

The name Fibonacci comes from a certain Leonardo de Pisa who wrote Liber Abaci in 1202. The Latin title in English means, "Book of Calculation." In a world that commonly used the abacus, Pisa's book conveniently shared how the use of the Arabic numerals, 0-9, could be effectively used, which set a new course economically, scientifically and mathematically. On the first page of this book was the phrase filius bonacci, which led to the nickname Fibonacci. The original page can be seen here.

Since his father was a customs officer, Fibonacci grew up in North Africa where he was greatly exposed to the Arabic numerals. At the time Europe continued to be immersed in the Roman numeral system and the need to use an abacus for any lengthy calculations. Their abacus was a board with lines upon which one moved pebbles. Complicating the economic system of Italy, Fibonacci's home, was the political division of the land into independent regions. Whenever merchants or bankers completed financial transactions between regions, complex conversions of money were required.

Fibonacci returned home to Italy in 1200 where he wrote his book Liber Abaci which was published in 1202. Understandably Fibonacci's book was revolutionary, simplifying the complex economic system of Europe.  However that is not what we remember him for today.

One of the examples in his book had to do with rabbits and an interesting equation found throughout nature, from rabbits to spirals to shells to the golden ratio. More on spirals, the golden ratio (and quilts) later!


My daughter and I used this art project to experience Fibonacci's mathematical proportions. Mine is below, which showcases the mathematical sequence, followed by a bit of simple art.

101_0001

However I think my daughter was quite a bit more creative than I was. She used the mathematical proportions to cut out her circles, then she designed this creative critter.

101_0002

Resources:

https://plus.maths.org/content/life-and-numbers-fibonacci

http://www.npr.org/2011/07/16/137845241/fibonaccis-numbers-the-man-behind-the-math

http://www.whatdowedoallday.com/2015/01/fibonacci-art-project.html

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