Authors: Marcos Georgallides
Article < The Six , Triple Concurrency Points , Line > is an extension of two Fundamental branches of geometry that of Perspectivity ( Desargues`s theorem , where 3 concurrency Points in a center of Perspectivity and 3 concurrency points on a line of Perspectivity , per two sides ) and that of Projective geometry ( Pascal`s theorem , with the 3 concurrency Points on a line , per two sides ) . Analyzing Extremum Principle ( Extrema ) on lines and Points , it was found that in any triangle ( three points only , which form a Plane ) and on the circumcircle exist one Inscribed and one Circumscribed , Extrema Triangle , such that on the six Extrema lines ( with a common concurrency point ) , both Perspectivity and Projective geometry concurrence on Common points on Extrema Lines . i.e. 18 lines concurrence in Six Points , per three , on a line , six triple concurrency points line. This Compact logic of Extrema exists on Points and in lines of Euclidean geometry. Article < Energy Laws follow Properties of Euclidean geometry > , is the deeper concept of Pythagoras theorem , where Conservation laws , referred to Physics and Mechanics , follow Euclidean moulds because these Principles belong to geometry as Points and Spaces ( geometry ) create Quantities and Qualities . Analyzing Euclid Spaces , it was found that on any two Equal and perpendicular , One dimensional Units , exists a Plane Formation ( A changeable and constant Tensor ) of constructing Squares , such that the Sum of Areas of the two Changeable Squares ( the Sum of the Squares of sides) is constant and equal to that of the circumscribed Square .The same also exists in Space Formation , where then , The Total Resultant Volume (cube of Resultant Sphere ) is the Sum of Changeable Volumes ( the Sum of the Cubes of Spheres of sides ). In Space Formation Changeable Volumes are Perpendicular each other , meaning that Conservation in Space ( Solid geometry ) occurs on Perpendiculars since first dimensional Units are Vectors . This geometrical mould of Conservation , is followed by Energy in Mechanics and Physics . i.e. The referred Energy Conservation laws in Mechanics and Physics , follow the Principle ( mould ) of Conserved Areas for Pythagoras` theorem on the moving machine of the two changeable Squares , and Conserved Perpendicular Volumes for Spaces on the Three Changeable Spheres .
Comments: 21 Pages.
[v1] 2012-03-02 10:47:14
Unique-IP document downloads: 179 times
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.