Mathematics in Ancient Civilizations

Ancient Civilizations

• Babylonians (1800 BCE):
  • Used a sexagesimal (base-60) number system
  • Developed arithmetic, algebra, and geometry
  • Invented the concept of zero (as a placeholder)
• Egyptians (2000 BCE):
  • Used a decimal (base-10) number system
  • Developed arithmetic and geometry
  • Used hieroglyphics to represent numbers
• Greeks (500 BCE):
  • Made significant contributions to mathematics
  • Developed the concept of irrational numbers
  • Famous mathematicians: Pythagoras, Euclid, and Archimedes

Development of Number Systems

• Hindu-Arabic Numerals (500 CE):
  • Developed in India and spread to the Middle East
  • Introduced the concept of zero as a number
  • Replaced Roman numerals in Europe
• Roman Numerals (500 BCE):
  • Used letters to represent numbers (I, V, X, L, C, D, M)
  • Limited arithmetic capabilities
• Mayan Numerals (200 CE):
  • Used a vigesimal (base-20) number system
  • Developed sophisticated arithmetic and astronomy

Middle Ages and Renaissance

• Fibonacci (1202 CE):
  • Introduced the Hindu-Arabic numeral system to Europe
  • Developed the concept of the Fibonacci sequence
• Renaissance Mathematicians (1500 CE):
  • Made significant contributions to algebra and geometry
  • Famous mathematicians: Luca Pacioli, Niccolò Tartaglia, and François Viète

Modern Developments

• Decimal System (1600 CE):
  • Became the standard number system in Europe
  • Facilitated arithmetic and scientific calculations
• Non-Decimal Systems (1900 CE):
  • Developed binary (base-2) and hexadecimal (base-16) number systems
  • Used in computer science and programming languages

Ancient Civilizations

• Babylonians developed a sexagesimal (base-60) number system around 1800 BCE, which is still used today for measuring time and angles.
• They contributed to arithmetic, algebra, and geometry, and invented the concept of zero as a placeholder.
• Egyptians used a decimal (base-10) number system around 2000 BCE and developed arithmetic and geometry, representing numbers using hieroglyphics.
• Greeks made significant contributions to mathematics around 500 BCE, developing the concept of irrational numbers, and notable mathematicians include Pythagoras, Euclid, and Archimedes.

Development of Number Systems

• The Hindu-Arabic numeral system, developed in India around 500 CE, introduced the concept of zero as a number and spread to the Middle East.
• This system replaced Roman numerals in Europe, providing a more efficient and versatile number system.
• Roman numerals, used from 500 BCE, relied on letters to represent numbers (I, V, X, L, C, D, M), but had limited arithmetic capabilities.
• The Mayan civilization developed a vigesimal (base-20) number system around 200 CE, demonstrating sophisticated arithmetic and astronomy skills.

Middle Ages and Renaissance

• Fibonacci introduced the Hindu-Arabic numeral system to Europe in 1202 CE and developed the concept of the Fibonacci sequence.
• Renaissance mathematicians, such as Luca Pacioli, Niccolò Tartaglia, and François Viète, made significant contributions to algebra and geometry around 1500 CE.

Modern Developments

• The decimal system became the standard number system in Europe around 1600 CE, facilitating arithmetic and scientific calculations.
• The development of non-decimal systems, such as binary (base-2) and hexadecimal (base-16) number systems, around 1900 CE enabled applications in computer science and programming languages.