Orthodiagonal quadrilaterals

The project presents the properties of orthodiagonal quadrilaterals, new author problems in respective field of geometry and their solutions. Also, in this project some properties of orthodiagonal quadrilaterals are transferred to octahedron and pyramid. These properties and problems can be used to develop respective products in the field of web design, computer graphics, 3D modeling, engineering and printing on a 3D printer. In addition, the describing properties of orthodiagonal quadrilaterals (including the proposed new solutions of classical problems, also new problems and their solutions), can be applied when studying geometry in schools and in the work of scientific mathematical societies.

Extension of the application range and parameters of the Airy pendulum for obtaining Lissajous curves

The Airy pendulum is a simple mechanical device for demonstrating the addition of two mutually perpendicular oscillations of the load which trajectory has the form of Lissajous curve. During experiments it was noticed that some Lissajous curves did not match with ones calculated according to the classical theory of Airy pendulum oscillations. In this project theoretical model of Airy pendulum load composite oscillations in specific conditions is developed and is used for the Lissajous curves form explanation. The proposed theoretical model is confirmed by the results of experiments in this project.

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