Abstract:

In this study, we give a synthetic approach to the quadrilateral “Kite”, or more specific to say, the “Right Kite”. It is mainly based on the definitions, postulates (axioms), propositions (theorem and constructions) from *the Euclid’s Elements*, which is known as one of the most successful and influential mathematical textbook attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c, 300 BC.

Linked up with the definitions of a “Right Kite” and the lines which meet the boundary of a said circle orthogonally described in the Pointcar´e Disk Model, we attempt to combine it in a mathematical task namely “Cryptography”. The application of Poincar´e Disk Model will be acted as a bridge to form a single key for encryption and decryption. Despite the single common trick we use, it leads to infinite possibilities by experiencing various and distinct mathematical skills in cryptography.

Last but not least, we would like to dedicate to the publication of Euclid’s Elements and the discovery of Euclidean Geometry so that we can admire the beauty of Mathematics. Our ultimate goal is to lay the new insight into some of the most enjoyable and fascinating aspects of geometry regarding to the most unaware quadrilateral, Kite

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