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| 5/24 |
| 2007/2/23-27 [Reference/Religion] UID:45801 Activity:moderate |
2/23 "Medieval Muslims made stunning math breakthrough"
http://news.yahoo.com/s/nm/20070223/sc_nm/architecture_patterns_dc
"Quasicrystalline patterns comprise a set of interlocking units whose
pattern never repeats, even when extended infinitely in all
directions, ..." Wow! Home Depot can probably charge a premium if it
carries these kinds of tiles.
\_ Cool! The medieval Arab world is actually responsible for lots of
math breakthroughs, many of which we use regularly. The most
obvious example I know if lies in the etymology of the word
algebra: http://en.wiktionary.org/wiki/algebra -dans
\- isnt the arab contribution to science sort of common knowledge?
[in addition to algebra, you'ld think cs people would know
algorithm]. but anyway, less common knowledge is the origin
of "sine", which was due to a "lost in transation" mistake
from sanskrit -> arabic -> latin due to "lossy compression".
it's kind of funny. obwiki:
http://en.wikipedia.org/wiki/History_of_trigonometric_functions#Etymology
If you are interested in "the fall of rome" and the rise of the
arabs" w.r.t. medieterranian culture, you may enjoy reading about
the PIRENNE THESIS.
If you are interested in the rise of the arab between the "fall"
of rome and the later rise of western "christendom" esp w.r.t.
w.r.t. mediterranian culture, you may enjoy reading about
the PIRENNE THESIS. I dont really know anything about art
history, but i like islamic art alot ... i think it is often
"design pattern" driven because they didnt waste so many
cycles on images of people in 2-d or 3-d, unlike the greeks,
romans, western eurpeans etc. that was for religious reasons.
why they didnt spend time on say landscapes [or if that is
even true] i am not sure.
\_ I think the Arab contribution to science is common knowledge
among mathematicians and science history buffs, but I think
they make up a pretty small segment of the general
population. :) -dans
\_ I think we should be more clear here. The Babylonians
and Persians, for example, were not Arab. Since the Arabs
were mostly nomads, I am not sure their contributions are
that great. I don't know if that last statement is
true, but nomadic horsemen aren't usually the type
to develop scientific breakthroughs.
\_ You'd have to check out the Arab world at it's height
in the 12-14th C. Before that it was barbarian tribal
time like you said and after that they were pretty much
under someone else's thumb right up to today.
\_ Cairo has been a city for longer than most of
the world has had literacy. It moved a few times,
due to the Nile moving around, but it has been
a center of learning for at least 4000 years. And
surely you have heard of the Library of Alexandria.
\_ You mean the library that the Greeks built?
\_ Yeah, I was going to point out that Persians (i.e.
modern-day Iran, typically Farsi vs. Arabic speakers.)
also contributed considerably to the Arab golden age,
but it felt like splitting hairs. But, yes, Persians
are distinct from Arabs. Was Babylon near its height
at the same time as the height of the Persian and Arab
empires? -dans
\_ We're all using arabic numerals.
\_ Which were developed in India.
\_ Huh? URL please?
\_ http://en.wikipedia.org/wiki/Arabic_numerals
Was that too difficult for you to find? |
| 5/24 |
|
| news.yahoo.com/s/nm/20070223/sc_nm/architecture_patterns_dc Reuters Medieval Muslims made stunning math breakthrough By Will Dunham Fri Feb 23, 6:32 AM ET WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday. By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasicrystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science. Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry. "Oh, it's absolutely stunning," Lu said in an interview. "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years." Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns. The walls of many medieval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs. "You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex" over time, Lu added. ISLAMIC ACHIEVEMENTS While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas. Lu said the new revelations suggest Islamic culture was even more advanced than previously thought. While traveling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasicrystalline Islamic tilings. The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide. Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasicrystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran. Joshua Socolar, a Duke university physicist, said it is unclear whether the medieval Islamic artisans fully understood the mathematical properties of the patterns they were making. "It leads you to wonder whether they kind of got lucky," Socolar said in an interview. "But the fact remains that the patterns are tantalizingly close to having the structure that Penrose discovered in the mid-70s." "And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show," Socolar said. Medieval Islamic artisans developed a pattern-making process for designing ornate tiled surfaces that allowed them to produce sophisticated patterns not seen in the West until centuries later, a new study suggests. Many walls of medieval Islamic buildings have ornate geometric star-and-polygon, or girih, patterns, often overlaid with a zig-zagging network of lines. This undated picture shows an archway from the Darb-i Imam shrine, Isfahan, Iran ( built in 1453 ) with two overlapping girih patterns. Republication or redistribution of Reuters content is expressly prohibited without the prior written consent of Reuters. Reuters shall not be liable for any errors or delays in the content, or for any actions taken in reliance thereon. |
| en.wiktionary.org/wiki/algebra algebras) 1 (mathematics) (uncountable) A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols. |
| en.wikipedia.org/wiki/History_of_trigonometric_functions#Etymology Almagest, deriving addition/subtraction formulas for the equivalent of sin(A + B) and cos(A + B). Ptolemy derived the equivalent of the half-angle formula sin^2(A/2) = (1 - cos)/2, and created a table of his results. His works also contain the earliest surviving tables of sine values and versine (1 - cosine) values, in 375 intervals from 0 to 90, to an accuracy of 4 decimal places. He used the words jya for sine, kojya for cosine, ukramajya for versine, and otkram jya for inverse sine. The words jya and kojya eventually became sine and cosine respectively after a mistranslation. Other Indian mathematicians later expanded Aryabhata's works on trigonometry. cubic equations using approximate numerical solutions found by interpolation in trigonometric tables. All of these earlier works on trigonometry treated it mainly as an adjunct to astronomy; Regiomontanus was perhaps the first mathematician in Europe to treat trigonometry as a distinct mathematical discipline, in his De triangulis omnimodus written in 1464, as well as his later Tabulae directionum which included the tangent function, unnamed. Copernicus, was probably the first to define trigonometric functions directly in terms of right triangles instead of circles, with tables for all six trigonometric functions; trigonometric series expansions of sine, cosine, tangent and arctangent. Using the Taylor series approximations of sine and cosine, he produced a sine table to 12 decimal places of accuracy and a cosine table to 9 decimal places of accuracy. |
| en.wikipedia.org/wiki/Arabic_numerals Eastern Arabic numerals are called "Indian numerals," aHr+q+a+m+ h+n+d+y+tm, (arqam hindiyyah) and a different set of symbols are used as numerals. Buddhist inscriptions from around 300 BC use the symbols which became 1, 4 and 6 One century later, their use of the symbols which became 2, 7 and 9 was recorded. Fibonacci that the Arabic numeral system was used by a large population. A distinctive "West Arabic" variant of the symbols begins to emerge in ca. A German manuscript page teaching use of Arabic numerals (Talhoffer Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer teaches them together with the Hebrew alphabet and astrology. Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. " The numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement was adopted identically into the numerals as used in Europe. The Latin alphabet running from left to right, unlike the Arabic alphabet, this resulted in an inverse arrangement of the place-values relative to the direction of reading. Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), and numbering pages in prefatory material in books. |