earn your daily wage first before abstractions

#OpenChallenge 

#mathematics 

Strict Note to the Mathematics Community

“Earn Your Daily Wage First, Then Think Abstraction”

The Revolution of Geometrifying Trigonometry by Sanjoy Nath

Prologue

Dear Mathematics People,

Engineers are not angry without reason.

They build bridges, weld beams, and measure tolerances in millimeters.

Yet the people who design mathematical languages for them live in clouds of n-dimensional abstraction.

You talk about infinity; they fight misaligned bolts.

Sanjoy Nath’s Philosophy of Geometrifying Trigonometry arises as a revolt from the shop floor a revolution against sterile abstraction, returning arithmetic to the Euclidean plane of daily life.

1. Learn Earning concrete Before You do Abstract

“Earn your daily salary first; then talk abstraction.”

Mathematics must justify itself through contact with real work.

Concrete geometry  not ornamental theory earns its keep.

When you sketch a structure, align two plates, interpret ratios as calipers,

you perform the real mathematics of life,

not symbolic display.

Nathism restores utility as the #16narrativesateveryreality2d  #moraltestoflogic moraltestoflogic

Whatever your cognition supports first do it everytime first 

Whatever your cognition supports last do it last lifelong #nathism 

#Ifyoulearnadditionbeforedivisiondoadditionfirst

#Ifyoulearndivisionlastdodivisionlastforwholelife

#BODMASVersusBOCDMAS

A theorem earns its right to exist only when it can build, align, or weld something real.

2. Real Numbers as Triangles

In the Geometrifying Trigonometry Number System, every real number is represented as a 2D Euclidean triangle.A caliper is defined as a triangle minus one dummy complementary edge:

\text{Caliper} = \text{Triangle} - 1 \text{ dummy complementary edge.}

Two visible edges embody a real relationship:

Denominator → Reference edge

Numerator → Gluer edge(or ourput edge)

Division is not an abstract quotient; it is a #politicianscannotdoit #aReferenceToGluerRelationship #ReferenceToGluerRelationship, a physical act of alignment and scaling to fit.

When multiplied, calipers glue onto one another:

(G_1/R_1) \times (G_2/R_2) \times \dots \times (G_n/R_n)

Each gluer  becomes the next reference .

The final gluer  is the output edge of the entire operation.

This cumulative structure forms a 2D Simplex,

the #GTSIMPLEX  the foundational object of Sanjoy Nath’s materialistic arithmetic.

3. The Engineering Meaning of “Gluing”

To mathematicians, gluing is a metaphor.

To engineers, gluing is welding and alignment.

In the real world, to multiply means to align and scale to fit.

To divide means to cut and reference.

To add means to assemble in calibrated order.

Hence:

All operations are non commutative

#allaritgmeticisnaturallynoncimmutstive

Sequence defines possibility.

Geometry defines logic.

4. Axioms of Materialistic Arithmetic

1. Addition is tougher than division.

It requires compatibility of calipers — geometric readiness for assembly.

2. Division is easiest.

It’s the first operation cognition understands — defining reference before gluing.

3. Multiplication is progressive gluing.

Each gluer becomes the next reference, constructing structure stage by stage.

4. All operations are non-commutative.

Reality proceeds through chronological geometry, not symbolic freedom.

---

5. Comparison with Classical Mathematics

Domain Classical Mathematics Geometrifying Trigonometry

Object Abstract number 2D Euclidean triangle

Operation Symbolic equation Geometric construction

Division Computed quotient Reference–Gluer pairing

Multiplication Algebraic scaling Align & scale to fit

Addition Commutative sum Sequential assembly

Philosophy Abstraction first Wage first, Reality first

---

6. Practical Horizon

Steel fabricators, CAD modellers, and BIM designers handle 4-symmetry geometry problems daily — concurrency, tolerance, and scale alignment.

Traditional mathematics offers tensors and topologies, but no visual clarity.

Geometrifying Trigonometry provides a Vocabulary of Precision — a consistent Euclidean representation where every ratio, angle, and weld corresponds to a real caliper system.

This becomes both a computational language and a visual ontology of reasoning for the engineer’s world

7. Historical Contrast: Thurston vs. Nath

William Thurston’s “gluing equations” built 3D hyperbolic manifolds elegant, abstract, unreachable.

Sanjoy Nath’s “gluing” constructs real triangles on the Euclidean plane immediately usable in fabrication and measurement.

Thurston studied ideal tetrahedra at infinity.

Nath studies real triangles on sheets of steel.

One explores infinity.

The other repairs machinery.

8. Philosophical Epilogue

“What you learn first, do it first for life.

What you learn last, do it last for life.”

Sanjoy Nath’s #FLFDo #LLLDo Principle

We divide before we add; we anchor before we extend.

Everything in this system is natural and non-commutative,because nature itself follows ordered construction reference before gluer, gluer before sum.

Abstraction once served logic; now it serves ego.

Geometrifying Trigonometry restores mathematics to labor, clarity, and the tangible intelligence of daily life.

Strict Note

 Earn your daily wage first. Then think abstraction.

Sanjoy Nath’s philosophy slaps the mathematics community awake.

It declares that mathematics without geometry is wordplay,and that geometry without calipering is blindness.

Specially #mechanicalengineer and #structuralengineering  Engineers are angry because mathematics abandoned them.Nath re anchors mathematics to its true workshop.the 2D Euclidean Plane, where logic earns its living through construction.

 #GeometrifyingTrigonometryRevolution.

#OpenChallenge to the Mathematics Community

#mathematicians 

#mathematics #GeometrifyingTrigonometry #BOCDMAS #Nathism

“Earn Your Daily Wage First, Then Think Abstraction.”

The Revolution of Geometrifying Trigonometry 

#materialisticarithmetic  by Sanjoy Nath

Prologue

Dear Mathematics People,

Engineers are not angry without reason.

They build bridges, weld beams, and measure tolerances in millimeters —

while mathematicians float in clouds of n-dimensional abstraction.

You talk about infinity;

they fight misaligned bolts.

Sanjoy Nath’s Philosophy of Geometrifying Trigonometry arises as a revolt from the shop floor a revolution against sterile abstraction returning arithmetic to the Euclidean plane of daily life.

1. Learn Earning Before Abstracting

“Earn your daily salary first; then talk abstraction.”

Mathematics must justify itself through contact with real work.Concrete geometry not ornamental theory earns its keep.

When you sketch a structure, align two plates, or interpret ratios as calipers,you perform the real mathematics of life not symbolic display.

#Nathism restores utility as the moral test of logic.

Whatever your cognition supports first, do it first every time.

Whatever your cognition supports last, do it last lifelong.

#BODMASVersusBOCDMAS

#IfYouLearnAdditionBeforeDivisionDoAdditionFirst

#IfYouLearnDivisionLastDoDivisionLastForWholeLife

A theorem earns its right to exist only when it can build, align, or weld something real.

2. Real Numbers as Triangles

In the Geometrifying Trigonometry Number System, every real number is represented as a 2D Euclidean triangle.

A caliper is defined as:

\text{Caliper} = \text{Triangle} - 1 \text{ dummy complementary edge}

Two visible edges embody a real relationship:

Denominator → Reference edge

Numerator → Gluer (or Output) edge

Division is not an abstract quotient; it is a Reference Gluer Relationship a physical act of alignment and scaling to fit.

When multiplied, calipers glue onto one another:

(G_1/R_1) \times (G_2/R_2) \times \dots \times (G_n/R_n)

Each gluer becomes the next reference.

The final gluer is the output edge of the entire operation.

This non cumulative structure forms a 2D Simplex the #GTSIMPLEX, the foundational object of Sanjoy Nath’s Materialistic Arithmetic.

3. The Engineering Meaning of “Gluing”

To mathematicians, gluing is a metaphor.

To engineers, gluing means welding and alignment.

In the real world:

To multiply means to align and scale to fit.

To divide means to cut and reference.

To add means to assemble in calibrated order.

Hence:

All operations are non commutative.

Sequence defines possibility. Geometry defines logic.

#AllArithmeticIsNaturallyNonCommutative

4. Axioms of Materialistic Arithmetic

1. Addition is tougher than division.

It requires compatibility of calipers — geometric readiness for assembly.

2. Division is easiest.

It’s the first operation cognition understands — defining reference before gluing.

3. Multiplication is progressive gluing.

Each gluer becomes the next reference, constructing structure stage by stage.

4. In reality All arithmetic operations are non-commutative.Reality proceeds through chronological geometry, not symbolic freedom.

5. Comparison with Classical Mathematics

Domain Classical Mathematics Geometrifying Trigonometry

Object Abstract number 2D Euclidean triangle

Operation Symbolic equation Geometric construction

Division Computed quotient Reference–Gluer pairing

Multiplication is gluing in #SanjoyNath #geometrifyingtrigonometry means #caddesign Algebraic align and scaling Align & scale to fit

Addition Commutative sum Sequential assembly

Philosophy Abstraction first Wage first, Reality first

6. Practical Horizon

Steel fabricators, CAD modellers, and BIM designers handle 4-symmetry geometric problems daily  concurrency, tolerance, and scale alignment.

Traditional mathematics offers tensors and topologies elegant but impractical.

Geometrifying Trigonometry provides a Vocabulary of Precision a consistent Euclidean representation where every ratio, angle, and weld corresponds to a real caliper system.

It becomes both a computational language and a visual ontology of reasoning for the engineer’s world.

7. Historical Contrast: Thurston vs. Nath

William Thurston’s “gluing equations” built 3D hyperbolic manifolds — elegant, abstract, unreachable.

Sanjoy Nath’s “gluing” constructs real triangles on the Euclidean plane immediately usable in fabrication and measurement.

Thurston studied ideal tetrahedra at infinity.

Nath studies real triangles on sheets of steel.

One explores infinity.

The other repairs machinery.

8. Philosophical Epilogue

“What you learn first, do it first for life.

#BODMAS

#BODMASPARADOX

#BODMASFALLACY

#bocdmas 

What you learn last, do it last for life.”

Sanjoy Nath’s #FLFDo #LLLDo Principle

We divide before we add; we anchor before we extend.Everything in this system is natural and non-commutative,because nature itself follows ordered construction reference before gluer, gluer before sum.Abstraction once served logic; now it serves ego.Geometrifying Trigonometry restores mathematics to labor, clarity, and tangible intelligence.

Strict Note

Earn your daily wage first. Then think abstraction.

Sanjoy Nath’s philosophy slaps the mathematics community awake.It declares that mathematics without geometry is wordplay,and geometry without calipering is blindness.Specially Mechanical and structural engineer Engineers are angry because mathematics abandoned them.Nath re anchors mathematics to its true workshop the 2D Euclidean Plane,

where logic earns its living through construction.

Strict note

Earn
Your
Daily
Wage
First
Then
Think
Abstraction

Dear mathematics peoples

Sanjoy Nath slaps abstraction
Sanjoy Nath's philosophy of Geometrifying Trigonometry number system slaps over fascinating n dimensional maths community with big blow

"Earn your daily salary first"
Dont talk abstraction craps

Engineers are top much angry on mathematics peoples
Math peoples get money for not helping engineering peoples.they are over busy wirh bull shit abstraction. Sanjoy Nath found that gap and attacked whole community of mathematics people with concrete real life daily use maths.
Look dear math peoples.your maths are so abstract that no real people can use that in daily life.Sanjoy Nath's philosophy of Geometrifying Trigonometry number system has given big blow to your abstraction craps.

Sanjoy Nath's philosophy focus on pure 2D euclidean geometry representation of real numbers and to express all arithmetic as 2D Euclidean plane GEOMETRY process of re interpreted arithmetic which is sanjoy Nath's philosophy of materialistic arithmetic and to do so first comes Geometrifying Trigonometry as foundations basis of reasoning and interpretation.
Sanjoy Nath's Geometrifying Trigonometry strictly works on 2D Euclidean plane and generates 2D simplex (GTSIMPLEX and GTLOCKEDSET BOLS Bunch of Line Segments things as mathematical objects) . Sanjoy Nath's philosophy of Geometrifying Trigonometry number system has entirely different target to do research. Sanjoy Nath's target is to express algebra like trigonometry expressions into 2D Euclidean geometry representation which are BOLS Bunch of Line Segments looks like 2D Euclidean plane graph G (V,E) objects. Sanjoy Nath's philosophy of real numbers are considered as triangles and all real Numbers are Triangles because 2 line segments edges in a triangle always form caliper. Caliper is defined as one edge removed from a (2D Euclidean plane) triangle. One edge of the caliper is reference line segment which is denominator object and other edge of the caliper object is gluer line segment which is numerator object. Every division operation in Sanjoy Nath's philosophy of real numbers are reference to gluer relationship. Denominator to numerator relationship are always reference to gluer relationship. Say there is any expression like
(G1/R1)×(G2/R2)×..............(Gn/Rn)
The last gluer line segment Gn is output line segment of whole multiplication. This whole chain construction looks like 2D simplex. Sanjoy Nath's Geometrifying Trigonometry considers its name as GTSIMPLEX
G1 line segment is consumed as reference R2
G2 line segment is consumed as reference R3
......
Consuming as reference line segments means construction of a glued similar triangle such that
Line segment G_i is exactly overlapping on R_I+1
This means next reference gluer caliper(triangle - one dummy complementary edge) is constructed keeping all proportion same but "aligned and scaled to fit operation". Engineering peoples call this multiplication operation as "aligned and scaled to fit operation" whereas mathematics people call
this same operation as "gluing on common edge".

🙏🙏🙏🙏🙏🙏

Strict note that this third dummy line segment is not any evaluation. This thitd dummy complementary line segment is only to complete the 2 edged caliper object to complete 2D triangle object. Real numbers in Sanjoy Nath's philosophy of Geometrifying Trigonometry number system is the ratio of length of numerator gluer edge to length of denominator reference line segment object. This process of reference to gluer ratio process is materialistic arithmetic (followed from Greek ancient mathematicians to curren Steel fabricators shop floor everwhere in engineering fitter welders terms)
Engineers almost always get angry on mathematics people because creating concrete GEOMETRY (ambiguity free language for GEOMETRY representation is not there but mathematics people are over busy with abstract super abstract super super over abstract abstraction things and real ground problems of 4 symmetry handling are still in dark age. Sanjoy Nath's Geometrifying Trigonometry philosophy started addressing vocabulary designing concrete systems ambiguity free concrete mathematics for Steel fabricators bim systems 4symmetry handling like situations of daily life in Steel fabricators and erection process geometry issues. Sanjoy Nath's Geometrifying Trigonometry address hardcore Steel structures bim geometry problems and Sanjoy Nath's gluing means real welding gluing where gluing represent real multiplication with "align and scaled to fit" which is practically a cad command. Sanjoy Nath's Geometrifying Trigonometry philosophy of real numbers is practically practical and no unnecessary abstraction done there.

Side note

Stage 1 cancer cells own intelligence versus stage 6 cancer cells own intelligence 😃😃😃🙏🙏🙏🙏
Cancer cells know and smile at human
Calipering the secret
Caliper is just 2 edge
2D Euclidean plane Triangle -1 dummy complementary edge= a caluper object
Sanjoy Nath's philosophy says
Axiom 1
Addition is tougher than division
Axiom 2
Division is easiest and human cognition understand division first which is reference to gluer relationship
Axiom 3
Multiplication is gluing decides stage wise gluer objects

Only after sufficient gluer objects in hand now use filters which you can add or which you cannot add.and addition need proper calipered order so
Everything are noncommutative
Strict note
Everything is noncommutative
Strict note that You cannot add things in order less ways

"Addition and rule'
Have you ever heard that??????
"Division and rule"
You heard that

Sanjoy Nath's philosophy of Geometrifying Trigonometry number system says it is natural

Natural
Natural
Natural

Only after a certain level of maturity of human's owns mind of cognition human will understand"addition is rule"

Sanjoy Nath's philosophy of Geometrifying Trigonometry number system (natural materialistic arithmetic)BOCDMAS is reality
🙏🙏🙏🙏🙏🙏

Sanjoy Nath's Division operation means construction of triangle on 2D Euclidean plane because joining the third dummy line segment through 2 free ends of a caliper construct a triangle. Triangle on 2D Euclidean plane and caliper object on 2D Euclidean plane are same things when interpreting with Sanjoy Nath's philosophy of real numbers because
2D Euclidean plane triangle -one dummy complementary edge= a caliper
Caliper= representation of reference to gluer relationship

________________________
Whereas
Thurston did different research
Thurston did not focus on plane Trigonometry
___________________________________
Thurston gluing is a mathematical technique introduced by William Thurston to construct 3 dimensional hyperbolic manifolds by gluing together ideal tetrahedra. This method involves solving a system of "gluing equations" that ensure the dihedral angles of the tetrahedra match up correctly at the edges where they are joined. This process allows for the study and creation of complex geometric shapes and has been applied to fields like low-dimensional topology and geometry, with ongoing research into its generalizations and applications.
How it works
Ideal tetrahedra: The building blocks are ideal tetrahedra, which are tetrahedra with vertices at infinity.
Gluing equations
The dihedral angles at the faces where the tetrahedra are joined must be made to match for the resulting manifold to be geometrically consistent.
Solving the equations: Mathematicians solve the "Thurston gluing equations" to find the values of the angles that satisfy these matching conditions.
Constructing a manifold: By finding a solution, a consistent geometric structure, such as a hyperbolic 3-manifold, can be constructed from the pieces.
Applications and extensions
Hyperbolic 3-manifolds: The technique is a fundamental tool for understanding and constructing these complex shapes, which are important in low-dimensional topology.
Geometric transitions: The method has been generalized to study transitions between different types of geometries, such as from hyperbolic to anti-de Sitter (AdS) geometry.
Computational methods: Computer programs have been developed based on these equations to help mathematicians study and visualize these geometric structures.
Generalizations: Researchers have extended the concept beyond hyperbolic geometry, for example, to explore non-commutative versions of the equations or to study other types of geometric structures.