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.

Explore the contributions of ancient civilizations, including Babylonians, Egyptians, and Greeks, to the development of mathematics, including number systems, arithmetic, and geometry.