Angle trisector, as validated to perform accurately over a wide range of device settings by a novel geometric forming process; also capable of portraying finite lengths that only could be approximated by means of otherwise applying a compass and straightedge to a given length of unity; that furthermore functions as a level whose inherent geometry could be adapted for many other uses such as being incorporated into the design of a hydraulic car lift.

Abstract

A newly proposed articulating invention, each of whose four constituent embodiments is designed to trisect any of a multitude of suitably described angles by means of becoming properly set to its designated magnitude; thus automatically portraying a motion related solution for the trisection of an angle that discloses complete routing details of a pathway that leads from such designated magnitude all the way back to its trisector; thereby discerning the whereabouts of certain intersection points which evade detection when attempting to otherwise locate them by means of applying only a straightedge and compass to an angle of such designated magnitude; furthermore projecting finite lengths of any trisector that bears cubic irrational trigonometric properties, being those that cannot be duplicated, but only approximated, when applying a straightedge and compass to a given length of unity; and being of a unique design that could be adapted to function as a level.

What is claimed is: 
     
         1 . A Euclidean formulation, being a practical means for representing upon just a single piece of paper an entire family of geometric construction patterns which can be exclusively derived from a specific sequence of Euclidean operations; wherein only a double arrow notation would need to be placed at some strategic location upon one of such geometric construction patterns, furthermore referred to as its representative geometric construction pattern, thereby making it possible to observe how the appearance of such drawing would change there due to modifications made to the size of an angle which appears elsewhere upon such drawing that becomes denoted algebraically by the Greek letter θ. 
     
     
         2 . A geometric forming process which theorizes that complete pathways which lead from device settings of an angle trisector all the way back to their corresponding trisectors furthermore could be shown to superimpose upon respective geometric construction patterns belonging to a specific Euclidean formulation; thereby validating:
 that such mechanism actually could portray a wide range of unique motion related solutions for the problem of the trisection of an angle;   that the Euclidean limitation of being unable to backtrack upon irreversible geometric construction patterns whose rendered angles amount to exactly three times the size of their respective given angles can be overcome by means of introducing motion; and   that the reason why the classical problem of the trisection of an angle cannot be solved is because any devised geometric construction pattern remains impervious to the effects of time.   
     
     
         3 . A mathematics demarcation whose geometric forming process portion, being that wherein applied motions can affect outcomes, alone is capable of portraying lengths which are of cubic irrational value; as opposed to its conventional geometric construction portion wherein finite lengths of such magnitudes instead only could be approximated by means of applying a straightedge to a given length of unity.