The Role of Muslims in the Formation and Development of Sciences (Part 27)
The Role of Arab and Muslim Scholars in Geometry
Another important area of mathematics where Muslim scholars have made significant contributions is geometry. This essential science, which is used in various applications, plays a vital role in religious matters related to time and direction, and has a considerable impact on the construction and development of buildings and cities.
It is important to note that geometry has been one of the most prominent aspects of human civilization. Humans have relied on this science to construct houses, prepare agricultural lands, and utilize it practically. It should be acknowledged that geometry is one of the innovations of Greek thought, with pioneers such as Plato, Pythagoras, Democritus, and Thales among its founders. Arab and Muslim scholars paid great attention to geometry, particularly applied geometry, which aligned with their scientific goals, while Romans showed indifference to it.
The first significant developments in this field by Arab and Muslim scholars occurred during the Abbasid Caliphate under the leadership of Abu Ja’far Mansur, whose reign lasted from 136-157 AH. During this time, Euclid’s Elements of Geometry, sometimes referred to as the “Pillars of Geometry,” was translated. Euclid truly deserves the title of “the father of geometry.” This work consists of fifteen books, four dealing with “geometric surfaces,” one on “proportional quantities,” one on “the ratio of surfaces,” three on “numbers” and “geometric representation,” one on “logic,” and five on “geometric solids.”
Undoubtedly, Arab and Muslim scholars were at the forefront of the development of plane geometry, led by Muhammad ibn Musa al-Khwarizmi (164-235 AH), who integrated geometric theories to solve algebraic problems in his book Hisab al-Jabr wa al-Muqabla. Hajjaj ibn Yusuf ibn Matar (170-220 AH) also translated and annotated Euclid’s Elements twice; the first version was titled “Al-Haruni,” and the second was referred to as “Al-Ma’muni.” Thabit ibn Qurra (221-288 AH), who was proficient in Syriac, Hebrew, and Greek, flawlessly translated Euclid’s Elements, which became a reliable reference for mathematicians in the Islamic world for a long time. He later authored an important book that explored the profound relationship between algebra and geometry, making substantial strides toward analytical geometry which was further developed by Omar Khayyam. René Descartes later established its rules.
Division of Arab and Muslim Scholars in Mathematics
Arab and Muslim scholars classified geometry into two categories that have been recognized and employed throughout various ages:
1. Rational Geometry: This type, known as theoretical geometry, can be understood through abstract reasoning. It was developed by Greek scholars, particularly Euclid.
2. Sensory Geometry: This branch involves geometry that can be perceived visually and understood tangibly, essentially practical geometry. This type of geometry is one of the notable contributions of Arab and Muslim scholars, particularly led by Al-Hasan ibn Haytham.
Al-Hasan ibn Haytham (354-430 AH) significantly emphasized practical geometry, as reflected in some of his writings, such as his article on “Extracting the Direction of the Qiblah,” another on “the necessity of geometry in religious matters,” and a third discussing “Calculating the Distance Between Two Cities in Geometric Terms.” He also authored a book examining “The Alignment of Buildings and Excavations Using Various Geometric Forms.”
In his research and discoveries in “optics,” Ibn al-Haytham applied both theoretical and practical geometry, determining points of reflection in spherical, cylindrical, and conical mirrors, whether “convex” or “concave.”
Arab and Muslim scholars significantly advanced Euclid’s geometry, particularly regarding the “parallel postulate,” which Euclid could not prove as a theorem. Ibn al-Haytham first addressed this postulate, followed by Omar Khayyam, and later Nasr al-Din al-Tusi (597-672 AH), who also investigated it. Although their efforts to find a definitive proof did not yield conclusive results, these investigations inspired European mathematicians in the modern era to develop alternative geometries, such as non-Euclidean geometry.
In summary, while Arab and Muslim scholars added only modestly to the theoretical geometry inherited from the Greeks, they engaged deeply with it, providing commentary as they perceived logical connections within the theorems and hypotheses, which could lead to new geometric theories. In contrast, in applied geometry, Arab and Muslim scholars excelled, evident from their numerous scientific and practical works. This expertise reflects their application of geometric theories in various fields, including industry, civil engineering, art, and construction.
The contributions of Al-Khwarizmi, Thabit ibn Qurra, Ibn Haytham, and Tusi played a pivotal role in the advancement of geometry and established them as pioneers in this field. Therefore, it is incumbent upon the youth of the Arab and Islamic worlds to follow in their footsteps, striving in research and work to uncover the universal laws created by Allah Almighty, thereby strengthening our faith based on knowledge and insight.
Muslims have also applied their geometric knowledge in constructing Islamic mosques and historical sites, the grand and intricate designs of which can still be admired across Islamic lands.
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