The Islamic Bulletin Volume X IX No. 24 Page 30 What Should be Taught: The principles of this discovery were elaborated centuries before by Islamic Persia’s great scholar, al-Biruni (d. 1050). Lavoisier was a disciple of the Muslim chemists and physicists and referred to their books frequently. What is Taught: The Greeks were the developers of trigonometry . What Should be Taught: Trigonometry remained largely a theoretical science among the Greeks. It was developed to a level of modern perfection by Muslim scholars, although the weight of the credit must be given to al-Battani. The words describing the basic functions of this science, sine, cosine and tangent, are all derived from Arabic terms. Thus, original contributions by the Greeks in trigonometry were minimal. What is Taught: The use of decimal fractions in mathematics was first developed by a Dutchman, Simon Stevin, in 1589. He helped advance the mathematical sciences by replacing the cumbersome fractions, for instance, 1/2, with decimal fractions, for example, 0.5. What Should be Taught: Muslim mathematicians were the first to utilize decimals instead of fractions on a large scale. Al-Kashi’s book, Key to Arithmetic, was written at the beginning of the 15th century and was the stimulus for the systematic application of decimals to whole numbers and fractions thereof. It is highly probably that Stevin imported the idea to Europe from al-Kashi’s work. What is Taught: The first man to utilize algebraic symbols was the French mathematician, Francois Vieta. In 1591, he wrote an algebra book describing equations with letters such as the now familiar x and y’s. Asimov says that this discovery had an impact similar to the progression from Roman numerals to Arabic numbers. What Should be Taught : Muslim mathematicians, the inventors of algebra, introduced the concept of using letters for unknown variables in equations as early as the 9th century A.D. Through this system, they solved a variety of complex equations, including quadratic and cubic equations. They used symbols to develop and perfect the binomial theorem. What is Taught: The difficult cubic equations (x to the third power) remained unsolved until the 16th century when Niccolo Tartaglia, an Italian mathematician, solved them. What Should be Taught: Cubic equations as well as numerous equations of even higher degrees were solved with ease by Muslim mathematicians as early as the 10th century. What is Taught: The concept that numbers could be less than zero, that is negative numbers, was unknown until 1545 when Geronimo Cardano introduced the idea. What Should he Taught: Muslim mathematicians introduced negative numbers for use in a variety of arithmetic functions at least 400 years prior to Cardano. What is Taught: In 1614, John Napier invented logarithms and logarithmic tables. What Should be Taught: Muslim mathematicians invented logarithms and produced logarithmic tables several centuries prior. Such tables were common in the Islamic world as early as the 13th century. What is Taught: During the 17th century Rene Descartes made the discovery that algebra could be used to solve geometrical problems. By this, he greatly advanced the science of geometry. What Should be Taught: Mathematicians of the Islamic Empire accomplished precisely this as early as the 9th century A.D. Thabit bin Qurrah was the first to do so, and he was followed by Abu’l Wafa, whose 10th century book utilized algebra to advance geometry into an exact and simplified science. What is Taught: Isaac Newton, during the 17th century, developed the binomial theorem, which is a crucial component for the study of algebra. What Should be Taught: Hundreds of Muslim mathematicians utilized and perfected the binomial theorem. They initiated its use for the systematic solution of algebraic problems during the 10th century (or prior). What is Taught: No improvement had been made in the astronomy of the ancients during the Middle Ages regarding the motion of planets until the 13th century. Then Alphonso the Wise of Castile (Middle Spain) invented the Aphonsine Tables, which were more accurate than Ptolemy’s. What Should be Taught: Muslim astronomers made numerous improvements upon Ptolemy’s findings as early as the 9th century. They were the first astronomers to dispute his archaic ideas. In their critic of the Greeks, they synthesized proof that the sun is the center of the solar system and that the orbits of the earth and other planets might be elliptical. They produced hundreds of highly accurate astronomical tables and star charts. Many of their calculations are so precise that they are regarded as contemporary. The AlphonsineTables are little more than copies of works on astronomy transmitted to Europe via Islamic Spain, i.e. the Toledo Tables. What is Taught: The English scholar Roger Bacon (d. 1292) first mentioned glass lenses for improving vision. At nearly the same time, eyeglasses could be found in use both in China and Europe. What Should be Taught: Ibn Firnas of Islamic Spain invented eyeglasses during the 9th century, and they were manufactured and sold throughout Spain for over two centuries. Any mention of eyeglasses by Roger Bacon was simply a regurgitation of the work of alHaytham (d. 1039), whose research Bacon frequently referred to. What is Taught: Gunpowder was developed in the Western world as a result of Roger Bacon’s work in 1242. The first usage of gunpowder in weapons was when the Chinese fired it from bamboo shoots in attempt to frighten Mongol conquerors. They produced it by adding sulfur and charcoal to saltpeter. What Should be Taught: The Chinese developed saltpeter for use in fireworks and knew of no tactical military use for gunpowder, nor did they invent its formula. Research by Reinuad and Fave have clearly shown that gunpowder was formulated initially by Muslim chemists. Further, these historians claim that the Muslims developed the first firearms. Notably, Muslim armies used grenades and other weapons in their defence of Algericus against the Franks during the 14th century. Jean Mathes indicates that the Muslim rulers had stock-piles of grenades, rifles, crude cannons, incendiary devices, sulfur bombs and pistols decades before such devices were used in Europe. The first mention of a cannon was in an Arabic text around 1300 A.D. Roger Bacon learned of the formula for gunpowder from Latin translations of Arabic books. He brought forth nothing original in this regard. What is Taught: The compass was invented by the Chinese who may have been the first to use it for navigational purposes sometime between 1000 and 1100 A.D . The earliest reference to its use in navigation was by the Englishman, Alexander Neckam (1157-1217). What Should be Taught: Muslim geographers and navigators learned of the magnetic needle, possibly from the Chinese, and were the first to use magnetic needles in navigation. They invented the compass and passed the knowledge of its use in navigation to the West. European navigators relied on Muslim pilots and their instruments when exploring unknown territories. Gustav Le Bon claims that the magnetic needle and compass were entirely invented by the Muslims and that the Chinese had little to do with it. Neckam, as well as the Chinese, probably learned of it from Muslim traders. It is noteworthy that the Chinese improved their navigational expertise after they began interacting with the Muslims during the 8th century. What is Taught: The first man to classify the races was the German Johann F. Blumenbach, who divided mankind into white, yellow, brown, black and red peoples. What Should be Taught: Muslim scholars of the 9th through 14th centuries invented the science of ethnography. A number of Muslim geographers classified the races, writing detailed explanations of their unique cultural habits and physical appearances. They wrote thousands of pages on this subject. Blumenbach’s works were insignificant in comparison. What is Taught:The science of geography was revived during the 15th, 16th and 17th centuries when the ancient works of Ptolemy were discovered. The Crusades and the Portuguese/Spanish expeditions also contributed to this reawakening. The first scientifically- based treatise on geography were produced during this period by Europe’s scholars. What Should be Taught: Muslim geographers produced untold volumes of books on the geography of Africa, Asia, India, China and the Indies during the 8th through 15th centuries. These writings included the world’s first geographical encyclopedias, almanacs and road maps. Ibn Battutah’s 14 th century masterpieces provide a detailed view of the geography of the ancient world. The Muslim geographers of the 10th through 15th centuries far exceeded the The Qur’an & Science (continued from page 27)
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