Geometry

Study by Vector Projection of a Construction Made with a Rule and Compass to Understand Squaring the Circle

Authors: José Rodrigo Alejandro Martinez Diaz
Comments: (Improper cover page stripped by ai.viXra.org Admin)

The conditions of the problem establish the definition of a right triangle whose angle subtends the opposite cathetus with a value equal to alpha = arctan (1/ sqrt{pi}). Starting from this main condition, a series of steps are proposed to compare the precision between two idealized methods that describe the construction of a circle and a square linked to the triangle mentioned above. The first approximation is made taking into account "valid" compass and ruler constructions to obtain such geometric figures. The second construction is based on the lengths obtained by intersecting the previously mentioned geometric figures by performing the vector analysis. In both cases, the areas of the circle and square obtained are compared to find out if they are equal.
Category: Geometry