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

One thing that stopped me is that:

" The other is his suggestion that the idea of number needed to be enlarged to include a new kind of number, namely ratios of magnitudes. For example, in ‛Umar’s view, the ratio of the diagonal of a square to the side, or the ratio of the circumference of a circle to its diameter (π), should be considered as new kinds of numbers."

Also, "parallel postulate follows from the other Euclidean postulates"

I never realized that it is the Muslim people who introduced the idea of positive real numbers. I always thought that our current math system probably came mostly from Europe, especially the algebra notations and definitions. and it's also very cool to challenge the Euclid's Element and say that the postulate actually follows from the other Euclidean postulates. It shows the spirit of the mathematician.

another thing is that: 

However, a culture’s acquisition of intellectual material from an alien culture is a complex process and not accomplished in one place by a few individuals. And D. Gutas has argued that Muslim acquisition of foreign learning during the early years of the ‘Abbasid reign was as much due to political and religious problems facing the early caliphs as it was to simple intellectual curiosity and love of learning for its own sake.

I think for ancient countries it is very common for the political situation to affect the scholars and acquisition of any learning materials from alien cultures. The foreign learning itself is a political thing and even Buddhism would not flourish if there were not some king in India that promoted the religion. All studies and learning need sponsorship and support from the government I think, for ancient countries. But it still surprises me that foreign learning would help solve the political or religious problems for the caliphs.

Third thing that surprises me is that they were even able to find the positions of the planets.

To my understanding it is not until the modern times with satellites that they could position the planets. but it's done in the 1400's. They also tried to estimate the Earth's circumference.

I think what I take from it is that we should really use our logics to derive anything, even with minimal materials at hand. Today in my practicum my SA asked them to calculate how many degrees is one radian and the students just figured it out with proportional thinking and basic logics. It is a really important skill for the scientific world; otherwise, humans could never accomplish so many amazing things.  So I'll definitely implement that in my own classroom as well. 

I think I could introduce the history of these significant scientists and explore a bit about how they approached problems and did their scientific research，how they challenged authority and made up their own ideas, and how they used creative thinking and logical thinking in finding all these solutions. The students should see how it's important to have these skills rather than just sitting in the classroom and copying down a bunch of notes/formulas to use directly.