Loading ...
Sorry, an error occurred while loading the content.

RE: [EMHL] Triangle const. (a,h_a,r) [was: ADMIN.: Links]

Expand Messages
  • Nikolaos Dergiades
    Dear Luis, Sorry. You are right. Best regards Nikos Dergiades ... ___________________________________________________________ Χρησιμοποιείτε
    Message 1 of 5 , Jun 12, 2009
    • 0 Attachment
      Dear Luis,
      Sorry. You are right.

      Best regards
      Nikos Dergiades

      > Dear Nikos Dergiades,
      >
      >
      >
      > Thank you very much. Garcia Capitan had already
      >
      > given me the same results privately.
      >
      >
      >
      > ===
      >
      > and the focii are
      > ( 0 , 2ar^2/(a^2-4r^2) )
      > ( 0 ,-2ar^2/(a^2-4r^2) )
      > ===
      >
      > Hum... didn't you forget the y_0?
      >
      >
      >
      > ( 0 , y_0 + 2ar^2/(a^2-4r^2) )
      > ( 0 , y_0 -2ar^2/(a^2-4r^2) )
      > ===
      >
      >
      > The directrices are(?) y = y_0 \pm u/e
      >
      >
      >
      > where
      >
      >
      >
      > e = eccentricity = \sqrt{1 + (v/u)^2}
      >
      >
      >
      > Now I would be able to finish the construction showed in
      >
      > the site.
      >
      >
      >
      > Best regards,
      >
      > Luis
      >




      ___________________________________________________________
      Χρησιμοποιείτε Yahoo!;
      Βαρεθήκατε τα ενοχλητικά μηνύματα (spam); Το Yahoo! Mail
      διαθέτει την καλύτερη δυνατή προστασία κατά των ενοχλητικών
      μηνυμάτων http://login.yahoo.com/config/mail?.intl=gr
    • Luís Lopes
      Dear Hyacinthists, Resending. From: qed_texte@hotmail.com To: hyacinthos@yahoogroups.com Subject: RE: [EMHL] Triangle const. (a,h_a,r) [was: ADMIN.: Links]
      Message 2 of 5 , Jun 12, 2009
      • 0 Attachment
        Dear Hyacinthists,



        Resending.





        From: qed_texte@...
        To: hyacinthos@yahoogroups.com
        Subject: RE: [EMHL] Triangle const. (a,h_a,r) [was: ADMIN.: Links]
        Date: Fri, 12 Jun 2009 16:10:45 +0000



        Dear Nikos Dergiades,

        Thank you very much. Garcia Capitan had already
        given me the same results privately.

        ===
        and the focii are
        ( 0 , 2ar^2/(a^2-4r^2) )
        ( 0 ,-2ar^2/(a^2-4r^2) )
        ===
        Hum... didn't you forget the y_0?

        ( 0 , y_0 + 2ar^2/(a^2-4r^2) )
        ( 0 , y_0 -2ar^2/(a^2-4r^2) )
        ===

        The directrices are(?) y = y_0 \pm u/e

        where

        e = eccentricity = \sqrt{1 + (v/u)^2}

        Now I would be able to finish the construction showed in
        the site.

        Best regards,
        Luis



        To: Hyacinthos@yahoogroups.com
        From: ndergiades@...
        Date: Fri, 12 Jun 2009 15:31:12 +0000
        Subject: Re: [EMHL] Triangle const. (a,h_a,r) [was: ADMIN.: Links]







        Dear Luis,

        If I understood what you want, then

        y_0 = a^2r/(a^2-4r^2)

        u = 4r^3/(a^2-4r^2)

        v = 2r^2/sqrt(a^2-4r^2)

        where a^2 > 4r^2 always

        and the focii are
        ( 0 , 2ar^2/(a^2-4r^2) )
        ( 0 ,-2ar^2/(a^2-4r^2) )

        Best regards
        Nikos Dergiades

        > Dear Hyacinthists,
        >
        >
        >
        > In Angel Montesdeoca Delgado's web page below one finds
        >
        > an interesting solution to the problem (a,h_a,r).
        >
        >
        >
        > In it there is the conic (actually a hyperbola)
        >
        >
        >
        > 4r^2x^2 - (a^2 - 4r^2)y^2 + 2a^2 ry - r^2(a^2 + 4r^2) = 0.
        >
        >
        >
        >
        > In order to find its intersection with a line parallel to
        > the
        >
        > directrix I would like to have the hyperbola expressed in
        > the
        >
        > standard form
        >
        >
        >
        > (y - y_0)^2/u^2 - x^2/v^2 = 1. (*)
        >
        >
        >
        > Is it possible to get (*) symbolically?
        >
        >
        >
        > As always, I really appreciate your help.
        >
        > Thank you for your time.
        >
        >
        >
        > Best regards,
        >
        > Luis
        >
        >
        >
        >
        >
        > To: Hyacinthos@yahoogroups.com
        > From: anopolis72@...
        > Date: Thu, 28 May 2009 21:59:12 +0000
        > Subject: [EMHL] ADMIN.: Links
        >
        >
        >
        >
        >
        >
        >
        > I have added to the list's LINKS Page:
        >
        > http://tech.groups.yahoo.com/group/Hyacinthos/links/
        >
        > a link to Angel Montesdeoca Delgado's web page
        >
        > http://webpages.ull.es/users/amontes/otrashtm/varios.htm
        >
        > It contains interesting triangle geometry files
        > in pdf format (in Spanish).
        >
        > Listmembers may add other links (of Geometry interest)
        >
        > Antreas
        >
        >
        >
        >
        >
        >
        >
        >
        >
        > __________________________________________________________
        > Conheça os novos produtos Windows Live! Clique aqui.
        > http://www.windowslive.com.br
        >
        > [Non-text portions of this message have been removed]
        >
        >
        >
        > ------------------------------------
        >
        > Yahoo! Groups Links
        >
        >
        > mailto:Hyacinthos-fullfeatured@yahoogroups.com
        >
        >
        >

        __________________________________________________________
        Χρησιμοποιείτε Yahoo!;
        Βαρεθήκατε τα ενοχλητικά μηνύματα (spam); Το Yahoo! Mail
        διαθέτει την καλύτερη δυνατή προστασία κατά των ενοχλητικών
        μηνυμάτων http://login.yahoo.com/config/mail?.intl=gr












        Novo Internet Explorer 8: mais rápido e muito mais seguro. Baixe agora, é grátis!
        _________________________________________________________________
        Deixe suas conversas mais divertidas. Baixe agora mesmo novos emoticons. É grátis!
        http://specials.br.msn.com/ilovemessenger/pacotes.aspx

        [Non-text portions of this message have been removed]
      Your message has been successfully submitted and would be delivered to recipients shortly.