Fw: Ha compartido una publicación - "*We'll arrive at the same time* The *tautochrone..."

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Fw: Ha compartido una publicación - "*We'll arrive at the same time* The *tautochrone..."

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> Para los que gustan de las matemáticas
 

> Peter Meadows ha compartido una publicación (https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2F110246755251547563856%2Fposts%2FEBmFgR4dtoq&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED)
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> Peter Meadows ha compartido la publicación de John Baez contigo.
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> John Baez
> We'll arrive at the same time
>  
> The tautochrone is a curve with a remarkable property: if you let some beads slide down it, they all reach the bottom at the same time!  Ignoring friction, that is.
>  
> Even better, this curve is just an upside-down cycloid!  The cycloid is the curve you get by rolling a wheel on a flat road and tracing the motion of a point on the rim.
>  
> This was proved by Huyghens in 1659.   He also showed that the time of descent equals the time it takes for a rock to fall a distance of π...
>  
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> Has recibido esta notificación porque Peter Meadows estaba en un círculo al que te habías suscrito. Quiero darme de baja (https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2Fsettings%2Funsubscribe%3Fueat%3DAJ7SsMm_dfBgvgKzczJrRDIsdfDdul88M13TegrzMwV1AdQbt60ABwjrVQETJNfvzyFqFBEJCFL0kHiY89oMipjRXUPZqcGo-XpfOmXcyKtzYWd6NDjHDwcLSa4Rb24R3VP31OVxVfarQpF4tgILISBwCKwjEtlCB2_qGpW004UYc4PzAE9o2dsZkZLt7NAXH7r53TlWr9wg&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED) de estos correos.
> Consejo de privacidad: protege tu información. Elimina tu firma electrónica antes de responder.
> Google Inc., 1600 Amphitheatre Pkwy, Mountain View, CA 94043 USA
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Re: Fw: Ha compartido una publicación - "*We'll arrive at the same time* The *tautochrone..."

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Gracias por compartir, maese @morplenauta

Vean la relacion que hay entre
http://en.wikipedia.org/wiki/Tautochrone_curve
y la
http://en.wikipedia.org/wiki/Brachistochrone_curve

Conozco mas la segunda, que practicamente dio origen al calculo variacional
(dos Bernoulli dieron solucion, una mas ingeniosa y particular, otra mas
general, esta ultima creo recordar dio pie al calculo variacional)

De ahi al principio de Fermat, al de Maupertuis, al de Hamilton,
lagrangianos, Euler-Lagrange, ah... que temas!!! Bueno, los que tienen
paciencia, saben que los estoy tratando en mi blog

Nos leemos!

Angel "Java" Lopez
@ajlopez


On Thu, Jan 29, 2015 at 9:04 AM, Edgar De Cleene [hidden email]
[squeakRos] <[hidden email]> wrote:

>
>
> Para los que gustan de las matem€ ¢Ã¡ticas
>
>
>
> Peter Meadows ha compartido una publicaci€ ¢Ã³n
> <https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2F110246755251547563856%2Fposts%2FEBmFgR4dtoq&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED>
>
> <https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2F110246755251547563856&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED>
> Peter Meadows ha compartido la publicaci€ ¢Ã³n de John Baez contigo.
>
> <https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2F117663015413546257905&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED>
> John Baez
> *We'll arrive at the same time*
>
> The *tautochrone* is a curve with a remarkable property: if you let some
> beads slide down it, they all reach the bottom at the same time!  Ignoring
> friction, that is.
>
> Even better, this curve is just an upside-down cycloid!  The *cycloid* is
> the curve you get by rolling a wheel on a flat road and tracing the motion
> of a point on the rim.
>
> This was proved by Huyghens in 1659.   He also showed that the time of
> descent equals the time it takes for a rock to fall a distance of € ¢Ï’ ...
> [image: imagen no mostrada]
> <https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2F110246755251547563856%2Fposts%2FEBmFgR4dtoq&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED>
>
> Has recibido esta notificaci€ ¢Ã³n porque Peter Meadows estaba en un
> c€ ¢Ã­rculo al que te hab€ ¢Ã­as suscrito. Quiero darme de baja
> <https://plus.google.com/_/notifications/emlink?emr=13516955515809553030&emid=CMjW0cjXuMMCFVjwjAodSEcAVw&path=%2Fsettings%2Funsubscribe%3Fueat%3DAJ7SsMm_dfBgvgKzczJrRDIsdfDdul88M13TegrzMwV1AdQbt60ABwjrVQETJNfvzyFqFBEJCFL0kHiY89oMipjRXUPZqcGo-XpfOmXcyKtzYWd6NDjHDwcLSa4Rb24R3VP31OVxVfarQpF4tgILISBwCKwjEtlCB2_qGpW004UYc4PzAE9o2dsZkZLt7NAXH7r53TlWr9wg&dt=1422516674527&ub=STREAM_POST_SUBSCRIBED&uob=STREAM_POST_SUBSCRIBED>
> de estos correos.
> *Consejo de privacidad:* protege tu informaci€ ¢Ã³n. Elimina tu firma
> electr€ ¢Ã³nica antes de responder.
> Google Inc., 1600 Amphitheatre Pkwy, Mountain View, CA 94043 USA
>
>
>  
>