Corpus ID: 203904955

The Triangle

@inproceedings{Guy2019TheT,
  title={The Triangle},
  author={R. Guy},
  year={2019}
}
  • R. Guy
  • Published 2019
  • Mathematics
  • If we label the vertices of a triangle with 1, 2 and 4, and the orthocentre with 7, then any of the four numbers 1, 2, 4, 7 is the nim-sum of the other three and is their orthocentre. Regard the triangle as an orthocentric quadrangle. Steiner's theorem states that the reflexions of a point on a circumcircle in each of the three edges of the corresponding triangle are collinear and collinear with its orthontre. This line intersects the circumcircles in new points to which the theorem may be… CONTINUE READING

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