System of Equations

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Questions and Answers

What is the fundamental concept represented by 'ระบบสมการ'?

  • Simultaneous equations (correct)
  • Complex numbers
  • Matrix multiplication
  • Quadratic formula

What is the term for 'equation system' in English?

  • System of equations (correct)
  • Equation group
  • System equation
  • Equation set

In mathematics, what does the term 'system of equations' refer to?

  • A group of unrelated equations
  • A set of equations with different solutions
  • Multiple equations with common solutions (correct)
  • A single linear equation with multiple variables

Which mathematical concept involves solving 'ระบบสมการ'?

<p>Linear systems (C)</p> Signup and view all the answers

What did German mathematician Carl Friedrich Gauss describe as the queen of mathematics?

<p>Number theory (A)</p> Signup and view all the answers

What type of numbers do number theorists primarily study?

<p>Rational numbers (A)</p> Signup and view all the answers

In number theory, what are prime numbers studied in relation to?

<p>Integers (C)</p> Signup and view all the answers

Which branch of mathematics is devoted primarily to the study of integers and arithmetic functions?

<p>Number theory (A)</p> Signup and view all the answers

What term was used in older usage to refer to number theory?

<p>Higher arithmetic (A)</p> Signup and view all the answers

In number theory, what kind of equations are studied as either in themselves or as solutions?

<p>Linear equations (D)</p> Signup and view all the answers

What is the term for 'equation system' in English?

<p>System of equations (B)</p> Signup and view all the answers

What is the earliest historical find of an arithmetical nature?

<p>Pythagorean triples (B)</p> Signup and view all the answers

What does Euclid IX 21–34 likely represent in terms of its origin?

<p>Pythagorean mathematics (C)</p> Signup and view all the answers

What is credited to the early Pythagoreans?

<p>The discovery of irrational numbers (D)</p> Signup and view all the answers

Which mathematical concept was exceptionally well developed in Babylonian mathematics?

<p>Babylonian algebra (B)</p> Signup and view all the answers

What did the broken clay tablet Plimpton 322 contain?

<p>Pythagorean triples (B)</p> Signup and view all the answers

What is the term 'arithmetical' commonly preferred as?

<p>Number-theoretic adjective (B)</p> Signup and view all the answers

What did late Neoplatonic sources state about Pythagoras's learning of mathematics?

<p>He learned mathematics from the Babylonians. (C)</p> Signup and view all the answers

What does the heading over the first column of the broken clay tablet Plimpton 322 suggest?

<p>A system of equations (D)</p> Signup and view all the answers

What does the use of the term 'arithmetic' for number theory suggest?

<p>A resurgence in French influence (C)</p> Signup and view all the answers

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Study Notes

Systems of Equations

  • ระบบสมการ represents the fundamental concept of a system of equations in mathematics.
  • A system of equations refers to a set of equations containing variables and constants, and the goal is to find the values of the variables that satisfy all equations.

Number Theory

  • Number theory involves the study of properties of integers and other whole numbers.
  • Number theorists primarily study properties of whole numbers, particularly prime numbers.
  • Prime numbers are studied in relation to their distribution, properties, and behavior.
  • Number theory is devoted to the study of integers and arithmetic functions.

Historical Development

  • The term "arithmetic" was used in older usage to refer to number theory.
  • The earliest historical find of an arithmetical nature is the Babylonian tablet Plimpton 322, which dates back to around 1900-1600 BCE.
  • The Plimpton 322 tablet contains a list of Pythagorean triples, suggesting that the Babylonians had a strong understanding of arithmetic and geometry.
  • Euclid IX 21-34 is believed to have originated from the early Pythagoreans.
  • The Pythagoreans are credited with developing arithmetic and geometry to a high level.

Notable Mathematicians

  • German mathematician Carl Friedrich Gauss described number theory as the "queen of mathematics".
  • Late Neoplatonic sources stated that Pythagoras learned mathematics from the Babylonians.

Terminology

  • The term "arithmetical" is commonly preferred as "number theoretical".
  • The term "system of equations" is used to describe ระบบสมการ in English.
  • The use of the term "arithmetic" for number theory suggests that the study of numbers and their properties is a fundamental aspect of mathematics.

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