I need those who want to present at GREAT day to include titles
and abstracts as they want them published in the GREAT day program with
their annotated bibliography.
A 4-d map of Suzukl's book: …
§4.4 Quick Answers
I don't have much more information about this section than what Suzuki
shares. My books have mostly failed me here. I don't expect
this to happen again (with the possible exception in early US
mathematics). Andalusia here refers to Islamic controlled
portions of the Iberian Peninsula. It includes, but is much
larger than the region currently called Andalusia.
Some of this work in Spain is done by people born there. On the
other hand, I don't think we'll see anything of contributions from
Christian Spain. The Muslims were controlling part of Spain from
711 to 1492 (see - something important did happen on that date).
For reasons I can't quite explain, I don't know that we'll say anything
about Spain after this. Somehow they manage to not be remembered
much in mathematics history. I think while they were there, and
in the places they controlled the longest, since they were established
for over 700 years [remember your country is less than 250 years
old], the culture was definitely unambiguously Islamic.
A good question - why are these books written? Some are for
teaching a general populace, and some are for teaching those who are
trying to figure out more - for research. It is definitely
relevant to consider what use of any particular book was intended.
How does religion affect mathematics? In particular, how does it
affect topics studied? Altars, logic, large numbers …
We hear repeatedly about commentaries - esp. with Euclid. One
answer to what the use of this is the same as there being many
textbooks today on the same subject. Another answer is that
different expositors do add in different ideas, and sometimes they are
of changing consequence.
When Suzuki refers to al-Jayyani's ratios providing the basis for a
rigorous formulation of the theory of real numbers, he is referring to
what you study of the real numbers in real analysis. I don't know
more details thank that, but I expect Suzuki sees something of limits
or comparisons in the ratios.
At this time and even still today, sexigesimals (minutes, seconds) are widely used in astronomy.
Muhammad was the first Caliph, I believe, and his successors continued that.
Not knowing any better, I'm willing to allow that maybe the
introduction to Mu'taman's Perfection may have said "much of this was
written by others, I'm just putting it here for reference". We
will never know.
Reasonably I get questions about the progress of education. I
know almost nothing about the history of education. So, for the
most part, I can't speak to questions like that.
Why is Euclidean geometry more emphasised today than spherical?
It works better on the small scale, but whenever you consider
something global, spherical geometry is unavoidable. al-Jayyani
is certainly not the first to write on spherical geometry. Much
had been done before, but he is the first to write about it out of the
context of astronomy of some kind.
Commercial arithmetic is that required for commerce - probably mostly accounting.
Remember quadrature is finding the area. Mu'taman attempted to find the area of an ellipse.
Here is an al'ud. Apparently they are extant and played today.
I expect if ibn Ezra's KNKH story is credible that KNKH would have
brought numeration along with other aspects of Indian mathematics.
I don't think Islamic names are to be interpreted based on position,
but based on words. "ibn" means "son of", "abu" means father of,
and the "al-" parts seem to be generally descriptors (wherefrom, jobs
&c).
We have seen combinations previously in Indian mathematics, and the
arithmetic triangle also in China, where they used it for binomial
coefficients.
Latin allowed the works of Islamic mathematics (in Arabic) to be read
in Europe, and in many cases the works of Greek mathematics, which had
been translated into Arabic, as well.
It is my impression that most of the mathematicians we have studied so
far have made a living by working for the government (whatever form
that took). Surely there are exceptions, but that seems most
common.
I looked up and found Berbers are people from North Africa. An
astrolabe is a mechanical device used for tracking the motions of the
sun and stars.
The library at Cordoba was destroyed, but some of the books seemed to have remained.
Much is known, and I know a few things, about mesoamerican mathematics,
but Suzuki chose not to include it. As with many of topics chosen
to not include, it would be rather easy to read on your
own.
"In the mid thirteenth century, Alfonso X founded School of Translators
in Toledo, where he compiled all the ancient books and manuscripts he
could and translated them from Greek, Latin, Arabic, and many other
languages into Castilian so as to not lose these invaluable texts. He
created a very culturally accepting atmosphere in Spain at the time,
and I think this is a big reason of why all these Islamic texts that
survived did just that."
Surely people can travel with animals and sea travel is also used in these times.
I don't know of any mathematics in the Qu'ran. (But it's worth
admitting the pi in the Bible is pretty inconsequential, too.)
We already discussed amicable numbers. Check earlier posts.
Aurillac is in France.
This not our first mention of a woman. We've seen mathematicians
and leaders. We will see more, but only as history allows.
We cannot make up history to suit our desires.
Aside from year nomenclature, the calendar used in these times in the
west is close to modern - ti's the Julian calendar. This goes
back to the time of Caesar. The Islamic calendar is lunar.
We discussed this before.
"Recent research paints a new picture of the debt that we owe to
Islamic mathematics. Certainly many of the ideas which were previously
thought to have been brilliant new conceptions due to European
mathematicians of the 16th, 17th, and 18th centuries are now known to
have been developed by Arabic/Islamic mathematicians around four
centuries earlier. In many respects, the mathematics studied today is
far closer in style to that of Islamic mathematics than to that of
Greek mathematics."