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

Re: [EMHL] A quartic

Expand Messages
  • xpolakis@otenet.gr
    ... == x^2y(ysinBsinC - zsin^2A)sinA + y^2z(zsinCsinA - xsin^2B)sinB + + z^2x(xsinAsinB - ysin^2C)sinC = 0 which looks like isosomething with pole (sinBsinC -
    Message 1 of 1 , Jun 6, 2001
    • 0 Attachment
      [APH]:
      >Let ABC be a triangle and P a point.
      >Denote angles (BPC) := t, (CPA) := u, (APB) := v,
      >
      >Which is the locus of P such that
      >
      > cott + cotu + cotv + cotw = 0
      >
      >where w = Brocard angle ?
      >
      >The locus is the curve with equation in normals:
      >
      >sinAsinBsinC[(xy)^2 + (yz)^2 + (zx)^2] - xyz(xsin^3A + ysin^3B + zsin^3C) = 0

      ==>

      x^2y(ysinBsinC - zsin^2A)sinA + y^2z(zsinCsinA - xsin^2B)sinB +

      + z^2x(xsinAsinB - ysin^2C)sinC = 0

      which looks like isosomething with pole (sinBsinC - sin^2A ::)

      and pivot (sinA ::)


      APH
    Your message has been successfully submitted and would be delivered to recipients shortly.