Newton straight
The Newton line is the straight line that runs in a convex square , which is not a parallelogram , through the centers of the two diagonals . Parallelograms must be excluded from this definition because the midpoints of the diagonals coincide in parallelograms and therefore do not define a straight line.
The two lines that connect the centers of opposite sides in a convex quadrilateral intersect at a point that lies on the Newton straight line. If the convex square is also a tangent square , then according to Newton's theorem the center of the inscribed circle is also on the Newton line.
literature
- Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics . MAA, 2010, ISBN 9780883853481 , pp. 108-109, 116-118 ( excerpt (Google) )
Web links
- Alexander Bogomolny: Bimedians in a Quadrilateral on cut-the-knot.org