Geometrifying Trigonometry Is Different from Vector Algebra

Refer

Geometrifying Trigonometry is Different From Vector Algebra

Sanjoy Nath(c) Algebraic Structure of Geometrifying Trigonometry REFER https://geometrifyingtrigonometry.quora.com/The-Forgotten-Line-Segments-in-Trigonometry

We have defined Several operations of Geometrifying Trigonometry which looks similar to that of Vector Algebra but the definitions of Equality , Definitions of Summations , Definitions of Toe Tips are all very much different and too much rigid in case of Geometrifying Trigonometry.

Although we use Vector Algebra to model several real life problems , We can use Geometrifying Trigonometry for several mathematical modeling systems to generate alternative identity conditions , or several types of visualization problems or to model scenario analysis where space planning is necessary

We have checked that many of such operations are not completely cross verified yet in CAD programming.We are working with checking of Associativity for all 7 types of * operations and also for Other operations.We are trying to search best algorithms or redefinitions regarding PIVOT , ALIGN,SCALE TO FIT of ∞ operation where as we have seen through simulations that ∞/ and ∞\ works best

Geometrifying Trigonometry

Geometrifying Trigonometry

Geometrifying Trigonometry:[Cos(Θ)]^6 Representations

SanjoyNaths Conjecture:Geometrifying Trigonometry: Tips of Line Segment (1+(Sin(Θ))^2)^0.5 and (1+(Cos(Θ))^2)^0.5 forms Cyclic Quadrilateral

Corollary:Geometrifying Trigonometry: Cos(Θ) x Sin(Θ)=Sin(Θ) x Cos (Θ) has 25% Chance to become equal

Corollary:Geometrifying Trigonometry: Cosec(Θ) x Cosec(Θ) - Cot(Θ) x Cot(Θ) = 1 represents PHPH - PBPB=P

Corollary:Geometrifying Trigonometry:Sec(Θ) x Sec(Θ) - Tan(Θ) x Tan(Θ) =1 That means BHBH-BPBP=B (The initial line segment considered as 1)

Corollary:Geometrifying Trigonometry:Tan(Θ) x Tan (Θ) is not Tan Squared Theta but it is BP * BP

Corollary:Geometrifying Trigonometry: Cos(Θ) x Cos (Θ) is not Cos Squared Θ it is HB*HB the line segment

Corollary :Geometrifying Trigonometry:Sin(Θ) x Sin (Θ) is not Sin Squared Θ , It is HP*HP

Theorem 10: Geometrifying Trigonometry :There are 6 Types of Equality in Geometrifying Trigonometry.≡ , = , ≈ , Æ , æ and ₧

HEP Arrangement is a Locked Set

Theorem 9:Geometrifying Trigonometry :Need definition of 1 and 0 for eiπ+1=0 Which is defined here (The initial line segment considered as 1)

Theorem 8:Geometrifying Trigonometry: Number of defined Line segments in HEP Arrangement is rank of the System

Theorem 6 :Geometrifying Trigonometry:There are Two Fundamental Types of Trigonometric Expressions Simple and Compound

Theorem 3++:Geometrifying Trigonometry:Every of Predefined line segments Locked on Locked Set HEP Arrangement has two Trigonometric Ratios involved

Theorem 7:Geometrifying Trigonometry: Every Compound Douplet String of Geometrifying Trigonometry Does not mean Reciprocal of Given Expression.

Theorem 3+:Geometrifying Trigonometry:The Division of Trigonometric Expression means a Star(*) Operation in String Duplets

Theorem 3:Geometrifying Trigonometry:The Multiplication of Trigonometric Expressions means a Star(*) Operation in Strings Duplets

Theorem 1 : Geometrifying Trigonometry :Contiguity of Intermediate Dot Operation is Worthless Other than First and Last Alphabet

Theorem 2: Geometrifying Trigonometry:Reciprocal String (Duplet) for Simple Ratios under Dot Operation is Reverse of that String(Duplet)

Strings in Geometrifying Trigonometry and interpretations(Part 2 HEA or HEP)

Circles Fourier Series and Geometrifying trigonometry GT String Formal Systems

Strings in Geometrifying Trigonometry and interpretations(Part 1 with Dots and Stars)

Operators , Their actions and Interpretations on GT String

Interpretation of Pythagoras Theorem in Geometrifying Trigonometry HBHB+HPHP=H (Line segment H Itself )

37 Line Segments and 10 Points Identified to Symbol set of Geometrifying Trigonometric Formal System

Automated Symbolic formulation of operations and formations due to operations on GT Strings in Geometrifying Trigonometry

Implementation of First order ,Second Order And Higher Order logic through Stringology on Geometrifying Trigonometry

Some more stringology with Geometrifying of Trigonometry

Combinatorial properties of Geometrifying trigonometry

Geometrifying Trigonometry Fundamental rules explained

Some First words on Geometrifying trigonometry

Geometrifying Trigonometry