Orixe (matemáticas)

A orixe dun sistema de coordenadas cartesianas

En matemáticas, a orixe dun espazo euclidiano é un punto especial, normalmente denotado pola letra O, usado como punto fixo de referencia para a xeometría do espazo circundante.


Coordenadas cartesianas

Nun sistema de coordenadas cartesianas, a orixe é o punto onde se cruzan os eixes do sistema.[1] A orixe divide cada un destes eixes en dúas metades, un semieixe positivo e outro negativo.[2] Despois, os puntos pódense localizar con referencia á orixe dando as súas coordenadas numéricas, é dicir, as posicións das súas proxeccións ao longo de cada eixe, xa sexa na dirección positiva ou negativa. As coordenadas da orixe son sempre todas cero, por exemplo (0,0) en dúas dimensións e (0,0,0) en tres.[1]


Outros sistemas de coordenadas

Nun sistema de coordenadas polares, a orixe tamén se pode chamar polo. Non ten coordenadas polares ben definidas, porque as coordenadas polares dun punto inclúen o ángulo formado polo eixe x positivo e o raio desde a orixe ata o punto, e este raio non está ben definido para a propia orixe. [3]

Na xeometría euclidiana, a orixe pódese escoller libremente como calquera punto de referencia conveniente.[4]

A orixe do plano complexo pódese referir como o punto onde se cruzan o eixe real e o eixe imaxinario. Noutras palabras, é o número complexo cero. [5]

Notas

  1. ↑ 1,0 1,1 Madsen, David A. (2001). Engineering Drawing and Design. Delmar drafting series. Thompson Learning. p. 120. ISBN 9780766816343. .
  2. ↑ Pontrjagin, Lev S. (1984). Learning higher mathematics. Springer series in Soviet mathematics. Springer-Verlag. p. 73. ISBN 9783540123514. .
  3. ↑ Tanton, James Stuart (2005). Encyclopedia of Mathematics. Infobase Publishing. ISBN 9780816051243. .
  4. ↑ Lee, John M. (2013). Axiomatic Geometry. Pure and Applied Undergraduate Texts 21. American Mathematical Society. p. 134. ISBN 9780821884782. .
  5. ↑ Gonzalez, Mario (1991). Classical Complex Analysis. CRC Press. ISBN 9780824784157. .

Véxase tamén

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