SANJOY NATH GEOMETRIFYING TRIGONOMETRY(C) HOW TO RUN AUTOMATED TRIGONOMETRY SIMULATOR DEMONSTRATION

Evaluation is replaced with Epicturization. Evaluation gives numerical values. That is not helpful for all engineering purpose. Engineers understand engineering drawings to the scales.Engineers need stl files , dxf files , IFC files , CAD files with real geometry. Numerical values graph is for finance peoples or for managers only.

EValuation dont tell all stories(special purpose use values and special purpose reasonable meaningfulness ) in expressions.
Euclidify? yes you can say.
Euclidification? yes you can say that also.
Geometrize ? yes you can say that also.
Geometrify? yes you can say that also.
Purpose is to do real product manufacturing and to visualize the outputs as real products.
Graph or chart on graph paper are not Euclidean Geometry thing.
Actually it is a purposeful parsing of trigonometry expressions and generating Euclidean Geometry from that expression(With rigorous symmetries well defined). We cannot allow ambiguity in construction protocols. Robot arm movements don't allow options for ambiguity in geometry.

GeoGebra file is here
(I have kept this video silent such that viewer can have unbiased view on operating the simulator for Automated Trigonometry)
I had to prepare the theory of Geometrifying Trigonometry formalized strong rigorous enough such that we can automate (RULER COMPASS LIKE) geometry construction of Euclidean Geometry from given Trigonometry expressions or algebra expressions.
We assume users know how to type trigonometry expressions in excel (spreadsheet) formula.

As Structural,CIVIL,Mechanical Engineers,Fashioners or Jewelry designer(product designer)need to generate CAD geometry (manufacturable cnc or dxf files to the scale) from text string(excel formula are also text strings) like expressions and it is tough for us to visualize the possibilities of geometry remains hidden inside trigonometry expressions.
GT is an algebra over line segments,points and triangles.
It has all operators of algebra like = + * ÷ whereas every of these are NON COMMUTATIVE but ASSOCIATIVE.

Theory takes the expressions as geometry, rational numbers as not ratio of numbers but considers as a transformation of given line segment to output line segments.Consider any rational number(Or Irrational number rationalized as numerator and denominator which are lengths of line segments). Numerator is the (length of)output line segment (repositioned or transformed due to multiplication of ratios in 2D plane)and the denominator is the length of given line segment. When two or more rational numbers (or rationalized irrational numbers)multiplied then theory says (Non commutative operation of multiplication) output of first ratio taken as the input of next ratio(multiplier) and the chain continues when several rational numbers are multiplied one after MULTIPLICATION SINCE ORDERED RATIOS in the factor generates different pictures after transformations) so forms pictures.
These pictures are GTSimplex(Geometrifying Trigonometry Simplex) since these are formed with glued triangles(Similar SEED TRIANGLES repositioned , reoriented , re scaled due to multiplications. Since 2D geometry is having 4 symmetries(2 for rotations and 2 for reflections) so every Trigonometric ratios are 4 types.Cos(Θ) is of 4 symmetries and as per these are A(Θ),B(Θ),C(Θ),D(Θ) CASE SENSITIVE ORDERED ALPHABETS taken as operators of Trigonometric ratios multiplications geometrically(Cremona 1860 AND also Maxwell Reciprocal Diagram 1860)rules of structural engineering Graphical Statics.
Sin(Θ) is taken as E(Θ),F(Θ),G(Θ) ,H(Θ) , Similarly Tan(Θ) is taken as I(Θ) , J(Θ) , K(Θ) , M(Θ).Sec(Θ) is taken as N(Θ),O(Θ),P(Θ),Q(Θ). Similarly 4 symmetries of Cosec(Θ) are denoted with R(Θ), S(Θ),T(Θ),U(Θ), for Cot(Θ) the symmetries are written as V(Θ), W(Θ), X(Θ),Y(Θ)
All case sensitive where L is the starting of the constructions procedures and L is the pre declared line segment

(Cos(Θ) ^ 2) + (Sin(Θ) ^ 2) = 1 transforms the string expressions as
L* A(Θ) * A( Θ) * Z + L* E(Θ) * E( Θ) * Z = L
Given Line Segment L = 1 (For Classical Trigonometry)) conventions

For simplicity of writing with only one SEEDS ANGLE Θ cases all triangulations GT Simplex generates with all similar triangles glued to each other due to multiplications of rational (or rationalized representations of irrational numbers) we can write Pythagoras Theorem like
LAAZ+LEEZ=L or LABZ + LEFZ=L
Starting L means 1 unit given line segment
or with all possible combinations of Cos(Θ) , Sin(Θ) which all generates different picture proofs of the cases with automated constructions in computer systems following parser Algorithm available in Autodesk Forums with Lisp Codes and also with C sharp Simulators.Since all the alphabets CAPITAL LETTERS used for basic cases and other cases for compound Trigonometry expressions like 1 + tan(Θ) is 'a' , swapping of Output line segment rotating 180 degrees about midpoint of output line segment at that stage.