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[2] viXra:2510.0151 [pdf] submitted on 2025-10-31 22:11:53
Authors: Teo Banica
Comments: 400 Pages.
This is an introduction to plane geometry, angles and trigonometry, starting from zero or almost. We first discuss basic plane geometry, with the main results regarding the triangles explained. Then we get into trigonometry, with the basic properties of the sine, cosine and tangent discussed. We then go on a more advanced discussion, using affine and polar coordinates, then complex numbers, and with a look into trilinear coordinates too. Finally, we get into calculus methods, with an even more advanced study of the trigonometric functions, and with some applications discussed too.
Category: Geometry
[1] viXra:2510.0137 [pdf] replaced on 2025-11-24 22:51:06
Authors: Yerkebulan Bolat
Comments: 40 Pages.
This paper is devoted to an in-depth study of the concept of the power of a point and its applications to the solution of olympiad-level geometry problems. The discussion encompasses the classical definitions of the power of a point, the radical axis, and the radical center, as well as their various generalizations --- including the interpretation of a point as a circle of zero radius, the notion of coaxial circles, and the linearity property of power differences. Detailed examples drawn from both national and international mathematical olympiads are presented to showcase the effectiveness of these methods in addressing both classical and modern geometric problems. Furthermore, the paper considers potential extensions and applications within a broader framework of elementary geometry, with particular emphasis on their value as practical tools for olympiad training and problem solving.
Category: Geometry
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