Questions and Answers
Which ancient civilization used a decimal (base10) number system?
Egyptians
Who introduced the HinduArabic numeral system to Europe?
Fibonacci
Which number system was developed in India and spread to the Middle East?
HinduArabic Numerals
Which civilization used a vigesimal (base20) number system?
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In which century did the decimal system become the standard number system in Europe?
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Which ancient civilization made significant contributions to mathematics, including the concept of irrational numbers?
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What was the main limitation of Roman Numerals?
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When were binary and hexadecimal number systems developed?
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Study Notes
Ancient Civilizations

Babylonians (1800 BCE):
 Used a sexagesimal (base60) number system
 Developed arithmetic, algebra, and geometry
 Invented the concept of zero (as a placeholder)

Egyptians (2000 BCE):
 Used a decimal (base10) 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

HinduArabic 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 (base20) number system
 Developed sophisticated arithmetic and astronomy
Middle Ages and Renaissance

Fibonacci (1202 CE):
 Introduced the HinduArabic 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

NonDecimal Systems (1900 CE):
 Developed binary (base2) and hexadecimal (base16) number systems
 Used in computer science and programming languages
Ancient Civilizations
 Babylonians developed a sexagesimal (base60) 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 (base10) 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 HinduArabic 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 (base20) number system around 200 CE, demonstrating sophisticated arithmetic and astronomy skills.
Middle Ages and Renaissance
 Fibonacci introduced the HinduArabic 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 nondecimal systems, such as binary (base2) and hexadecimal (base16) number systems, around 1900 CE enabled applications in computer science and programming languages.
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Description
Explore the contributions of ancient civilizations, including Babylonians, Egyptians, and Greeks, to the development of mathematics, including number systems, arithmetic, and geometry.