Concoide de Durero

Concoide de Durero, ideada por el pintor alemán

La concoide de Durero, (también llamado Dürer), es una variante de una concoide o curva algebraica plana, nombrada así en honor a Alberto Durero. No es una concoide verdadera.

Construcción

Se parte de dos rectas perpendiculares entre sí, con el punto de intersección O, que se consideran los ejes de coordenadas con origen O (0, 0). Sean los puntos Q = (q, 0) y R = (0, r), que se mueven sobre los ejes de tal manera que q + r = b sea una constante. En la recta QR, extendida según sea necesario, se marcan los puntos P y P' a una distancia fija a de Q. El lugar geométrico de los puntos P y P' es la concoide de Durero.[1]​

Propiedades

La curva tiene dos componentes, asintóticos a las líneas Cada componente es una curva racional . Si a>b hay un bucle, si a=b hay una cúspide en (0,a).

Los casos especiales incluyen:

  • a=0: la línea y=0;
  • b=0: la línea se empareja con el círculo

Historia

Fue descrita por el pintor alemán y matemático Alberto Durero (1471@–1528) en su libro Underweysung der Messung (S. 38), llamándola Ein muschellini.

Véase también

Referencias

  1. ↑ Lawrence, J. Dennis (1972), A catalog of special plane curves, Dover Publications, p. 157, ISBN 0-486-60288-5, (requiere registro) .

Bibliografía

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