Arabic Mathematics

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\celsius }[0]{} \newcommand {\degree }[0]{} \newcommand {\ohm }[0]{} \newcommand {\npnoround }[0]{\nprounddigits {-1}} \newcommand {\npnoroundexp }[0]{\nproundexpdigits {-1}} \newcommand {\npunitcommand }[1]{\ensuremath {\mathrm {#1}}} \newcommand {\tri }[0]{\triangle } \newcommand {\l }[0]{\ell } \newcommand {\P }[0]{\mathcal {P}} \newcommand {\R }[0]{\mathbb {R}} \newcommand {\Q }[0]{\mathbb {Q}} \newcommand {\Z }[0]{\mathbb Z} \newcommand {\N }[0]{\mathbb N} \newcommand {\ph }[0]{\varphi } \newcommand {\vec }[0]{\mathbf } \newcommand {\d }[0]{\,d} \newcommand {\egmil }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_person.pdf}\hspace {0.5mm}}} \newcommand {\eghuntho }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_fish.pdf}\hspace {0.5mm}}} \newcommand {\egtentho }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_finger.pdf}\hspace {0.5mm}}} \newcommand {\egtho }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_lotus.pdf}\hspace {0.5mm}}} \newcommand {\eghun }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_scroll.pdf}\hspace {0.5mm}}} \newcommand {\egten }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_heel.pdf}\hspace {0.5mm}}} \newcommand {\egone }[1]{\multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_stroke.pdf}\hspace {0.5mm}}} \newcommand {\egyptify }[7]{ \multido {\i =1+1}{#1}{\includegraphics [scale=.1]{egyptian/egypt_person.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#2}{\includegraphics [scale=.1]{egyptian/egypt_fish.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#3}{\includegraphics [scale=.1]{egyptian/egypt_finger.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#4}{\includegraphics [scale=.1]{egyptian/egypt_lotus.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#5}{\includegraphics [scale=.1]{egyptian/egypt_scroll.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#6}{\includegraphics [scale=.1]{egyptian/egypt_heel.pdf}\hspace {0.5mm}} \multido {\i =1+1}{#7}{\includegraphics [scale=.1]{egyptian/egypt_stroke.pdf}\hspace {0.5mm}} \hspace {.5mm} } \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument } \newcommand {\degree }[0]{\ensuremath {^\circ }} \newcommand {\celsius }[0]{\ifmmode ^\circ \mathrm {C}\else $^\circ $C\fi } \newcommand {\ohm }[0]{\ifmmode \Omega \else $\Omega $\fi }$

Dunham leaves a pretty big gap after Chapter 5, which he covers just a little bit in the epilogue to the chapter. During the years between Heron (we’ll say after 150 AD) and Cardano (in the 1500s), people were still doing mathematics, of course! During this period, mathematics was being studied mostly in the Middle East and India. Our second reading helps us get a better sense of the contributions of Arabic mathematicians during this time period. The optional third reading gives an example of a scholar in this area talking briefly about how misconceptions about Arabic mathematics can still be hanging around even now.

Readings

First reading: Dunham, Chapter 5, pages 121 - 132

Second reading: Arabic Mathematics: forgotten brilliance?

Third reading: (Optional!) Recent Work On the History of Mathematics

Questions

How many of Archimedes’ works were translated into Arabic? $\answer [given]{2}$

Why did Arabic mathematicians use trigonometric tables?

For examples of algebra problems. To teach school children. In astronomy. In building projects.