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Evergreen Journey of Mathematics: From Stone Age to AI

 Evergreen Journey of Mathematics: From Stone Age to AI




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2.7. Progress of Mathematics in Arabian countries (2000 - 200 BC)

During the period from 2000 to 200 BC, the Arabian countries, particularly the regions now encompassing modern-day Saudi Arabia, Jordan, Yemen, and Iraq, played a significant role in the development and preservation of mathematics. Arabian mathematics emerged as a result of the diverse cultural exchanges and contributions from various civilizations, including the Mesopotamians, Egyptians, Greeks, and Indians. These mathematical advancements were later transmitted to Europe, contributing to the European Renaissance.

The Arabian mathematicians built upon the foundations laid by earlier civilizations and made significant contributions to various branches of mathematics, including arithmetic, algebra, trigonometry, and number theory. They were particularly interested in practical applications and focused on solving real-world problems.

Extract from work of Arabians

One of the notable achievements of Arabian mathematics was the preservation and translation of Greek and Indian mathematical texts. During the Islamic Golden Age, which began in the 8th century AD, scholars in the Arabian countries translated and preserved numerous Greek mathematical works, such as the works of Euclid and Archimedes, which had a profound impact on the development of mathematics in the region.

Arabian mathematicians made advancements in arithmetic, including the decimal number system. They adopted and expanded upon the Indian numeral system, introducing numerals we use today, including the concept of zero. The Arabian mathematicians also developed sophisticated methods for arithmetic operations, including addition, subtraction, multiplication, and division, along with techniques for calculating square roots and solving problems involving fractions.

Arabian numeral table

Algebra flourished under the Arabian mathematicians. They extended and refined the algebraic techniques inherited from the Indians and Greeks, further developing symbolic notation and solving equations of higher degrees. Mathematicians such as Al-Khwarizmi, who is often referred to as the "Father of Algebra," made substantial contributions in this field. Al-Khwarizmi's work, including his treatise on algebra called "Kitab al-Jabr wal-Muqabala," laid the foundation for the systematic study of algebra and provided a framework for solving both linear and quadratic equations.

Trigonometry also saw significant progress in the Arabian countries. Scholars like Al-Battani and Al-Jayyani refined and expanded upon the trigonometric concepts inherited from the Greeks and Indians. They developed trigonometric functions, tables, and formulas, and applied them to solve practical problems in fields such as astronomy, surveying, and navigation. These advancements were later transmitted to Europe and played a crucial role in the development of Western trigonometry.

Arabian mathematicians also contributed to number theory, particularly in the study of integers and divisibility. They made advancements in algorithms for prime factorization, which had practical applications in cryptography and encryption. They explored the properties of prime numbers, divisibility rules, and the relationships between integers, making significant contributions to number theory.


Ancient Arabian work 

The Arabian mathematicians also excelled in the field of geometry, building upon the Greek foundations. They explored geometric principles, including the properties of shapes and spatial relationships, and applied them to practical applications, such as architecture and geometric constructions.

The Arabian mathematicians played a pivotal role in the preservation, translation, and further development of mathematics during the Islamic Golden Age. These works not only preserved the knowledge of earlier civilizations but also added original contributions, fostering the development and transmission of mathematical knowledge across cultures. Their advancements in arithmetic, algebra, trigonometry, number theory, and geometry influenced subsequent mathematical traditions, including the European Renaissance. The work of these mathematicians laid the foundation for future advancements and helped shape the mathematical landscape of the world.

2.8. Roman civilization (200 BC - 200 AD)

The contributions of the Roman civilization to the development of mathematics are very significant, particularly in the areas of practical mathematics, engineering, and applied sciences. Although the Romans were not known for their great mathematical discoveries like the Greeks or Indians, their practical applications and mathematical methods played a significant role in their everyday lives and the advancement of their empire.

One of the notable contributions of the Romans was the development and widespread use of the Roman numeral system. This numeral system, which employed combinations of letters to represent numbers, allowed for efficient record-keeping, trade transactions, and architectural calculations. The Romans used symbols such as I, V, X, L, C, D, and M to represent numbers, with different combinations and positions denoting different values.


Roman numerals

While not as suitable for complex mathematical calculations as other numeral systems, the Roman numerals persisted as a primary method of recording numbers and dates for centuries.

Practical mathematics played a crucial role in Roman society. The Romans were skilled in measurements, particularly in construction and engineering. They developed methods for surveying and measuring land, constructing roads, aqueducts, and buildings, and ensuring accurate alignments and proportions. The Roman engineers utilized mathematical principles to create complex structures, such as the Colosseum, which required precise calculations for the arches, columns, and dimensions.

Roman engineers and architects applied geometric principles to their construction projects. They used tools such as plumb lines, levels, and compasses to ensure straight lines, right angles, and symmetrical designs. The mastery of geometric principles allowed the Romans to build monumental structures that still stand today as testament to their mathematical expertise.

Human Crane used in ancient Rome

The Romans were also adept at practical arithmetic, especially in the context of commerce and finance. They developed efficient methods for calculation, such as the abacus, which allowed for speedy addition, subtraction, multiplication, and division. Roman merchants and traders relied on these arithmetic techniques for measuring quantities, calculating profits, and conducting business transactions.

Roman mathematicians and engineers made significant contributions to applied sciences, particularly in the field of astronomy. They developed calendars, such as the Julian calendar introduced by Julius Caesar, which were based on astronomical observations and mathematical calculations. The calendar was designed to align with the solar year and regulate religious festivals and civic events.

Furthermore, Roman mathematicians and astronomers made contributions to trigonometry, primarily for practical applications in surveying and navigation. They devised methods for calculating distances and angles using triangulation and developed tables for solving trigonometric problems.

Roman Calendar

The mathematical achievements of the Romans were not extensively documented in dedicated mathematical treatises but were preserved in their architectural designs, engineering practices, and practical applications. The Romans were skilled at assimilating and implementing mathematical knowledge from other cultures, incorporating Greek, Egyptian, and Mesopotamian mathematical principles into their own practices. Their contributions in practical mathematics, measurements, arithmetic, geometry, and applied sciences influenced subsequent cultures and civilizations, and their architectural achievements continue to inspire awe and admiration to this day.

.....TO BE CONTINUED

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