An introduction to the mathematics of the Golden Age of medieval Islam

The first thing that struck me is that the Islamic world made so many contributions in science and mathematics but we rarely talk about them. And a lot of these Islamic mathematicians were actually pioneers in a lot of areas in Math. The modern word of algorithm actually comes from the name al-Khwārizmī. This shows the significant contribution from al-Khwārizmī to the mathematical world. One thing we can do in our classroom is to have a research project just on the life and contribution he made to the mathematical world.

The second thing I notice is the construction of a map of the known world back then. Al-Khwārizmī was a really versatile mathematician in the sense that he worked on a lot of different areas in mathematics. I was surprised that Muslims already knew that the Earth is actually a sphere and not a flat surface. People like Al-Khwārizmī worked on mapping a spherical world onto a plane surface. One can imagine how much information is needed and compiled to create this map. Note that in modern maps, the size of a piece of land on a flat surface may actually be very different in the real world since the world is on a spherical surface. 

The third thing is the contribution of al-Kāshī on the estimation of 2π. He was accurate to 16 decimal places and this itself is an amazing feat. He used perimeter of inscribed and circumscribed polygons to estimate the value of 2π. This is actually similar to the method done by Liu Hui of China. It is interesting that different civilizations with totally different backgrounds can come up with mathematical ideas that agree with each other. Some of these civilizations did not even have a chance to interact with each other. Using perimeter of inscribed and circumscribed polygons to estimate the value of 2π would be a very fun activity to do in class. Of course we will be using polygons with only a few sides so that students can get a glimpse of how the mathematicians of ancient civilizations went about estimating the value of 2π.