28 citations · 41 across the 24 of their papers we have counts for
26 papers
Besant quadrilaterals
Alan Horwitz
We solve the following problem of W.H. Besant using a formula for the coefficients of an ellipse inscribed in a quadrilateral, : \enquote{If an ellipse be inscribed in a quadril…
Midpoint Diagonal Quadrilaterals
Alan Horwitz
A convex quadrilateral, , is called a midpoint diagonal quadrilateral if the intersection point of the diagonals of coincides with the midpoint of at least one of the diagon…
The foci and rotation angle of an ellipse, , as a function of the coefficients of an equation of
Alan Horwitz
First, we give a formula for the foci of an ellipse, , as a function of the coefficients of an equation of (see Theorem <ref>T2</ref>). To prove Theorem <ref>T2</ref>, we…
When is an ellipse inscribed in a quadrilateral tangent at the midpoint of two or more sides ?
Alan Horwitz
In "Quartic Coincidences and the Singular Value Decomposition" by Clifford and Lachance, Mathematics Magazine, December, 2013, it was shown that if there is a midpoint ellipse(an e…
A generalization of parallelograms involving inscribed ellipses, conjugate diameters, and tangency chords
Alan Horwitz
A convex quadrilateral, , is called a midpoint diagonal quadrilateral if the intersection point of the diagonals of coincides with the midpoint of at least one of the diagon…
Ellipses of minimal eccentricity inscribed in midpoint diagonal quadrilaterals
Alan Horwitz
In an earlier paper of the author, we showed that there is a unique ellipse of minimal eccentricity, , inscribed in any convex quadrilateral, . Using a different approach i…