In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form The polar equation of this curve is of the form . Devil's curves were discovered in 1750 by Gabriel Cramer, who studied them extensively. The name comes from the shape its central lemniscate takes when graphed. The shape is named after the juggling game diabolo, which was named after the Devil and which involves two sticks, a string, and a spinning prop in the likeness of the lemniscate.
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| - Corba del diable (ca)
- Curva del diablo (es)
- Devil's curve (en)
- Courbe du diable (fr)
- Duivelscurve (nl)
- Curva do diabo (pt)
- 魔鬼曲線 (zh)
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| - En geometria, una corba del diable és una corba definida al pla cartesià per una equació de la forma Les corbes del diable eren estudiades profundament per Gabriel Cramer. El nom ve de la forma que pren la seva gràfica. Sembla que el nom de diable de la corba vingui del joc anomenat diàbolo, que empra dos pals, una corda, i un carret amb una forma semblant a la d'aquesta corba. La confusió ve del fet que la paraula italiana diabolo vol dir 'diable'. (ca)
- Se llama curva del diablo o del diábolo a la cuártica siguiente en cartesianas: En polares: En la figura, las asíntotas están marcadas en rojo, y tienen las direcciones , que no dependen de a. Las ramas laterales cortan el eje X en los puntos (10a,0) y (-10a,0) (es)
- La courbe du diable a été étudiée en 1750 par Cramer et en 1810 par Lacroix. (fr)
- De duivelscurve is een vlakke meetkundige figuur die voor het eerst bestudeerd werd door de Zwitserse wiskundige Gabriel Cramer. De figuur bevat in het midden een gedeelte in de vorm van een diabolo. Via de Italiaanse vertaling, diablo, een woord dat ook duivel betekent, kreeg deze curve haar naam duivelscurve. (nl)
- Na geometria, curva do diabo é uma curva definida no plano cartesiano na equação da forma As curvas do diabo foram estudadas profundamente pelo matemático suíço Gabriel Cramer. O nome deriva da forma que a sua lemniscata central é assumida quando é representada graficamente. A forma foi nomeada em homenagem ao brinquedo chinês diabolo, composto por duas baquetas, uma corda e um suporte giratório que aparenta a lemniscata. A confusão resultou do facto da palavra italiana diavolo significar "diabo". (pt)
- 魔鬼曲線為方程式如下的平面曲線 加布里尔·克拉默曾對魔鬼曲線有許多研究。 魔鬼曲線得名自它中間的雙紐線，此形狀得名自雜耍遊戲扯鈴，扯鈴的外形類似雙紐線。但扯鈴的英文為diabolo，而義大利文的diabolo即為魔鬼。 (zh)
- In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form The polar equation of this curve is of the form . Devil's curves were discovered in 1750 by Gabriel Cramer, who studied them extensively. The name comes from the shape its central lemniscate takes when graphed. The shape is named after the juggling game diabolo, which was named after the Devil and which involves two sticks, a string, and a spinning prop in the likeness of the lemniscate. (en)
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| - En geometria, una corba del diable és una corba definida al pla cartesià per una equació de la forma Les corbes del diable eren estudiades profundament per Gabriel Cramer. El nom ve de la forma que pren la seva gràfica. Sembla que el nom de diable de la corba vingui del joc anomenat diàbolo, que empra dos pals, una corda, i un carret amb una forma semblant a la d'aquesta corba. La confusió ve del fet que la paraula italiana diabolo vol dir 'diable'. (ca)
- In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form The polar equation of this curve is of the form . Devil's curves were discovered in 1750 by Gabriel Cramer, who studied them extensively. The name comes from the shape its central lemniscate takes when graphed. The shape is named after the juggling game diabolo, which was named after the Devil and which involves two sticks, a string, and a spinning prop in the likeness of the lemniscate. For , the central lemniscate, often called hourglass, is horizontal. For it is vertical. Is , the shape becomes a circle.The vertical hourglass intersects the y-axis at . The horizontal hourglass intersects the x-axis at . (en)
- Se llama curva del diablo o del diábolo a la cuártica siguiente en cartesianas: En polares: En la figura, las asíntotas están marcadas en rojo, y tienen las direcciones , que no dependen de a. Las ramas laterales cortan el eje X en los puntos (10a,0) y (-10a,0) (es)
- La courbe du diable a été étudiée en 1750 par Cramer et en 1810 par Lacroix. (fr)
- De duivelscurve is een vlakke meetkundige figuur die voor het eerst bestudeerd werd door de Zwitserse wiskundige Gabriel Cramer. De figuur bevat in het midden een gedeelte in de vorm van een diabolo. Via de Italiaanse vertaling, diablo, een woord dat ook duivel betekent, kreeg deze curve haar naam duivelscurve. (nl)
- Na geometria, curva do diabo é uma curva definida no plano cartesiano na equação da forma As curvas do diabo foram estudadas profundamente pelo matemático suíço Gabriel Cramer. O nome deriva da forma que a sua lemniscata central é assumida quando é representada graficamente. A forma foi nomeada em homenagem ao brinquedo chinês diabolo, composto por duas baquetas, uma corda e um suporte giratório que aparenta a lemniscata. A confusão resultou do facto da palavra italiana diavolo significar "diabo". (pt)
- 魔鬼曲線為方程式如下的平面曲線 加布里尔·克拉默曾對魔鬼曲線有許多研究。 魔鬼曲線得名自它中間的雙紐線，此形狀得名自雜耍遊戲扯鈴，扯鈴的外形類似雙紐線。但扯鈴的英文為diabolo，而義大利文的diabolo即為魔鬼。 (zh)
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