Article response: Episodes in the Mathematics of Medieval Islam

 "His (Al-Khwārizmī ) other famous work, written before his Arithmetic, is his Kitāb al-jabr wa l-muqābala (The Book of Restoring and Balancing), which is dedicated to al-Ma’mūn. This book became the starting point for the subject of algebra for Islamic mathematicians, and it also gave its title to serve as the Western name for the subject, for algebra comes from the Arabic al-jabr. " (p.9)

Now we know why "algebra" is called algebra. I think it is great to tell my students how we name this subject as "algebra". By telling this story, the name of this subject "algebra" is no longer arbitrary. All children like to hear stories, at the same time, they could easily remember the word "algebra" as well as "al-jabr". "al-jabr" has the meaning of balancing. This makes sense. We are trying to keep the equation in balanced when finding the unknown numbers.

"The other is his (‛Umar al-Khayyāmī) suggestion that the idea of the 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 (square root of 2) or the ratio of the circumference of a circle to its diameter (π), should be considered as new kinds of numbers. This important idea in mathematics amounted to the introduction of positive real numbers and, as was the case with the parallel postulate, this was communicated to European mathematicians through the writings of the pseudo-Naṣīr al-Dīn al-Ṭūsī." (p.16)

This is another thing that I did not know before. It was Umar who suggested to include more types of numbers, such as some irrational numbers. I could also introduce this historical story to my students when I draw the Venn diagram as below:

"The observatory, as the scientific institution we know today, was born and developed in the Islamic world. Here is a part of the sextant (or perhaps quadrant) at the observatory in Samarqand where al-Kāshī worked. It was aligned in the north–south direction and was 11 meters deep at the south end. Thus an astronomer sitting between the guide rails could have seen the stars crossing the meridian even in the daytime while assistants sitting on either side held a sighting plate through which he could observe the transits of heavenly bodies. It was at this observatory that the greatest star catalog since the time of Ptolemy was compiled" (p.21)

Amazing! I didn't know that the observatory was born and developed in the Islamic world. I believe that children all like to visit the observatory. I will show them photos or let them watch videos about this observatory. I am always thinking of how I can integrate some astronomical knowledge while teaching mathematics. For example, space systems can be taught when teaching patterns and cycles. Many interesting Math problems are related to astronomy. I think I will design some interesting practice questions which combine mathematics with astronomy for my students.