The main focus is disseminating research results regarding the pencil of ellipses inscribing arbitrary convex quadrilaterals. In particular, the author proves that there is a unique ellipse of maximal area, EA, and a unique ellipse of minimal eccentricity, EI, inscribed in Q.
The main focus is disseminating research results regarding the pencil of ellipses inscribing arbitrary convex quadrilaterals. In particular, the author proves that there is a unique ellipse of maximal area, EA, and a unique ellipse of minimal eccentricity, EI, inscribed in Q.
Alan Horwitz holds a Ph.D. in Mathematics from Temple University in Philadelphia, PA, USA and is Professor Emeritus at Penn State University, Brandywine Campus where he served for 28 years. He has published 43 articles in refereed mathematics journals in various areas of mathematics. This is his first book.
Inhaltsangabe
1. Locus of Centers, Maximal Area, and Minimal Eccentricity. 2. Ellipses inscribed in parallelograms. 3. Area Inequality. 4. Midpoint Diagonal Quadrilaterals. 5.Tangency Points as Midpoints of sides of Q. 6. Dynamics of Ellipses inscribed in Quadrilaterals. 7. Algorithms for Inscribed Ellipses. 8.Non-parallelograms. 9. Parallelograms. 10. Bielliptic Quadrilaterals. 11. Algorithms for Circumscribed Ellipses. 12. Related Research and Open Questions.
1. Locus of Centers, Maximal Area, and Minimal Eccentricity. 2. Ellipses inscribed in parallelograms. 3. Area Inequality. 4. Midpoint Diagonal Quadrilaterals. 5.Tangency Points as Midpoints of sides of Q. 6. Dynamics of Ellipses inscribed in Quadrilaterals. 7. Algorithms for Inscribed Ellipses. 8.Non-parallelograms. 9. Parallelograms. 10. Bielliptic Quadrilaterals. 11. Algorithms for Circumscribed Ellipses. 12. Related Research and Open Questions.
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