Mathematics of Medieval Islam

 The first thing that really surprised me about this readings was when it described al-Khwarizmi as developing the Hindu-Arabic numeral system that we use today in The Book of Addition and Subtraction According to the Hindu Calculation. Abstractly, I knew that our decimal system was of Hindu origin and the ciphers we used for digits was Arabic, but it never occurred to me to imagine a single person developing those symbols. What an intriguing work of creativity, to develop distinct, meaningful symbols for digits. It might be an interesting project to work with a class and come up with your own set of digits, trying to symbolize "oneness" and "twoness" in the symbol. This draws back to a previous reading for this course from Alice Major discussing the personality of numbers. What sort of symbol would best represent the way we in Canada now understand each digit?

The next piece of the book which gave me pause, I must admit, was the quote from al-Biruni, "I was compelled to participate in worldly affairs, which excited the envy of fools, but made the wise pity me." It's such a cheeky comment and so reflective of the fascination that mathematicians have for their subject! While this may not have direct teaching value, I do think that it's a good illustration of the fact that people have found math interesting outside of its value in "worldly affairs" for centuries. I am definitely stealing the quote for my own use!

The final element of this introduction which thoroughly shocked me was the fact that al-Kashi calculated the decimal fractional notation of tau so precisely! I can't imagine trying to perform a calculation on a polygon with over eight hundred million sides. I think is a useful piece of information when instructing calculus students, helping them understand the truly revolutionary idea of limits at infinity. In most classes I have seen, teachers mention the method of circumscription and do an example or two, usually no more precise than a hexagon or perhaps an octagon. Suggesting to students to model their work after al-Kashi might give them both an appreciation for the mathematics of infinity as well as a reverence for the dedication of the Arabic mathematicians to astronomical precision.