 |
 |
Geometry |
|
Authors: Radhakrishnamurty Padyala
A geometrical proof of Ptolemy's theorem is presented. It shows the equality of the sum of the areas of the rectangles formed from the lengths of opposite sides of a cyclic quadrilateral to be equal to the area of the rectangle formed from the lengths of the diagonals. Introducing symmetry by choosing one of the component triangles of the quadrilateral to be an equilateral triangle, we prove the theorem for different cases. We then show that the specific case of maximum area configuration corresponds to that of a kite. By changing the kite configuration to that of a rectangle, we derive Pythagoras theorem as a special case of Ptolemy's theorem.
Comments: 9 Pages.
Download: PDF
[v1] 2020-05-02 02:23:00
Unique-IP document downloads: 618 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|