The theory of a convex quadrilateral and a circle that forms "Pascal points" - the properties of "Pascal points" on the sides of a convex quadrilateral

@inproceedings{Fraivert2016TheTO,
  title={The theory of a convex quadrilateral and a circle that forms "Pascal points" - the properties of "Pascal points" on the sides of a convex quadrilateral},
  author={David Fraivert},
  year={2016}
}
Euclidean geometry is one of the oldest branches of mathematics – the properties of different shapes have been investigated for thousands of years. For this reason, many tend to believe that today it is almost impossible to discover new properties and new directions for research in Euclidean geometry. In the present paper, we define the concepts of “Pascal points”, “a circle that forms Pascal points”, and “a circle coordinated with the Pascal points formed by it”, and we shall prove nine… Expand
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References

SHOWING 1-6 OF 6 REFERENCES
Lessons in geometry
Lessons in Geometry I, Plane Geometry
  • 2008
G
  • D. Gleizer, Ed.] Geometrical Miniature, Moscow, Prosveshenie, (in Russian)
  • 1990
Complex Numbers in Geometry
Geometry Revisited
  • NML-19, Mathematical Association of America, Washington, DC
  • 1967