How can we draw a line segment of length 1000 x (Cos(Θ))^1.3 with pure Autocad?

[SanjoyNath]

Dear Experts,

How can we draw a line segment of length 1000 x (Cos(Θ))^1.3 with pure Autocad? 

Example Take Θ=30 degrees

Pure Autocad, Fractional Powers Of Trigonometry,Constructions Protocol

Only to use Constructions Protocols(CAD commands like Line , Circle , Snap , Stretch , Align , Scale To Fit , Rotations , Mirror,Scaling ALLOWED)

We cannot use Algebra , Coordinates , Calculus , Series , Complex numbers , Vectors etc... for this purpose

We are not going back to Ruler and Compass days. But for my project of Sanjoy Nath's Geometrifying Trigonometry(C) i need to write program on Autocad[upto now these are done in Auto Lisp successfully and we could achieve these without algebra] and only with pure CAD commands]

https://forums.autodesk.com/t5/autocad-forum/thanks-to-autocad-for-geometrifying-trigonometry-narray...

Now we are stuck at fractional powers.We are not at all allowed to use calculator and spreadsheet.We are not allowed to use Algebraic systems of Trigonometry. We are not allowed to use complex numbers.

Only thing allowed for us is using Autocad Commands(Geometry Commands Only).

How can we draw the line segments of 1000 x (Cos(Θ))^K        where  n< K < (n+1)             , that means K is fractional.

We have achieved everything with Pure Autocad for + , - , x ÷ , n th Powers of all kinds.

Now we need to find fractional powers with Pure Autocad Only (No Algebra , No series Solutions , No Complex numbers to use)

Only to use Constructions Protocols(CAD commands like Align , Scale To Fit , Rotations , Mirror,Scaling ALLOWED)

[Alfred.NESWADBA]

Hi,

>> How can we draw a line segment of length 1000 x (Cos(Θ))^1.3

>> with pure Autocad?

Start command _LINE, pick the first point, then positiont the cursor to show the direction of your line segment and use this lisp statement for the length (whereas angle is assumed to 30° as you stated as sample):

(* 1000.0 (expt (cos (* (/ 30.0 180.0) 3.14159)) 1.3))

- alfred -

[j.palmeL29YX]

What about using the internal calculator (command CAL):

Command: line

Specify first point: pick any coordinate
Specify next point or [Undo]: 'cal
>>>> Expression: 1000*(cos(30d)^1.3)

Resuming LINE command.

Specify next point or [Undo]:  829.xxx-xxxxxxxx   (it is the result of the calculated Expression)

Specify next point or [Undo]: ENTER

Command:

cadder

[SanjoyNath]

Thank you @j.palmeL29YX  , You have taken interest in this very interesting project ,

I asked this to my Research Guide. Journal Editor also rejected the use of any kind of calculator.This need to go to full (Pure feature of Autocads Construction Protocol)

Even internal Calculator of Autocad uses Gregory series , Taylor's Series etc...) So not allowed

Only Pure Autocad Commands like Line , Circle , Offset , Scale , Align , Scale To Fit , Rotate , (No precalculated Stretch) , Snap is allowed (no precalculation is allowed)      Mirror is allowed

One thing more. Please look Sanjoy Nath's Geometrifying Trigonometry(C) , where you will see that + , - x ,÷ are completely redefined in Autocad commands. No Calculator is used for that.

Thank you @Alfred.NESWADBA  also

[Erense]

Next to what @Alfred.NESWADBA did you can also enter the 'formula' into the AutoCAD Calculator and use the outcome.

Give the Line command, Enter the formula in the calculator, click 'paste value to commandline', enter the value.

Formula in calculator looks like this: 1000*(cos(30)^1.3) with the result of 829.449255.

Or does the AutoCAD calculator also count as 'calculator'? But it still is Pure AutoCAD and not the Windows calculator 😉

"Edit"

I see I have missed your latest remark while typing my answer. so Never Mind.

[SanjoyNath]

Dear @Erense ,

This is a research problem for Computational Geometry which will completely place Autocad on the Rulers Sit of Mathematics even above the Big Mathematical genius

Internal calculators which use Series solutions or lookup tables are not allowed.

But it still is Pure AutoCAD and not the Windows calculator 😉         I thought same , but internal calculator use Algebra and Lookup inside that.So we cannot use that for this project particularly.

This is pure Autocad commands output for whole numbers power of Cos(Θ)

SanjoyNath(C)GeometrifyingTrigonometry(C)GeometrificationOfTrigonometry(C)GeometricProofOfTrigonometry(C)POLYGONNUMBERING(C)SETUPSOUTLINESDONE_PYTHAGORUSSanjoyNathCosPowerSpiral(C)COT_Theta.png

[SanjoyNath]

Dear Experts of Autocad And Computational Geometry,

Thank you Autodesk for such good Product

AUTOCADs Model Space is an infinite REAL (PRINTABLE)Euclidean Plane 

We dont want to disturb that with Complex Numbers (IMAGINARY JUGAD which has destroyed the beauty of Pure Trigonometry for 370 years)Complex numbers helped electrical and electronics engineers and reduced the power of Mechanical Engineers , Civil Engineers , Structural engineers , Architects since that removed the scope of many real geometry (Effective for Real Ground CORE engineering) Complex numbers have suppressed the beautiful millions of effective possible engineering pictures and stress flow diagrams present inside Trigonometric Expressions Which we are reviving back through Pure Autocad Programming(Autolisp programming)[Long discussions are there in Autolisp Forum]

For Architects Sanjoy Nath's Geometrifying Trigonometry(C) Algebraic Structure and Pure Autocad Framework  has generated 128 types of pictures for Pythagorian Theorems which were hidden inside Euclidean Geometry and was suppressed due to over use of complex numbers distracted Trigonometry biased towards Electrical and Electronics Engineers and depriving Mechanical Engineers , Civil Engineers , Surveyors, Architects .These will help in automated Truss load path planning and also for Pre Triangulation 

Thank you @dbhunia               Fantastic programs are written to generate physical plate folding pictures from Powers of Trigonometric ratios.Remaining works are going on.These are not using any kind of infinite series.These are not using any complex numbers to generate Euler's Formula Effect(Very fundamental for Engineering) . 

Thank you @CodeDing  for Line Segment manipulations done on the Quad Tree Datastructure which is implemented in pure Autolisp without using any algebra

Target Problems area where Sanjoy Nath's Geometrifying Trigonometry(C) focus now

Plate Nesting,Profile Orientations,Edge unique nomenclature,Irregular Shapes Classification and Unique Standards of Nomenclature for material and scrap handling,Folded plates management and orientability,Pre stress path Triangulations,Pre moment flow Geometry,Material handling in SAP/ERP  through unique shape nomenclature , Human face unique polygon equation systems for patterns mining           SYNTHETIC PRE TRIANGULATION OF POLYGONS(Regular or Irregular),Proof Mechanisms, Automated geometry generations for Higher Algebraic Objects

And Surely This will generate all types of super pictures of Any given Trigonometric Expressions (Even Series) to visualize the feasibility , foldability , constructability , weldability , cuttability to assemble into particular Assembly shapes of Steel Structures. This is a PROOF MECHANISM which geometrically proves (USING PURE AUTOCAD AND NO COMPLEX NUMBER NEVER) 

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No one(Even great experts in the field of geometry and API) have a framework to communicate in Standard UNIVERSAL NAME . Because no one tried to make UNIVERSAL NAMING of polygons edges.This is the FUNDAMENTAL REASON FOR COMMUNICATION GAP for Geometry Programmers

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It is very interesting Question.Several times we see that Angles Get 4 different types of Top Face while we change rotations and effective Top surfaces are 2 there. Start Handle and End Handle of the Angle changes the possibility of the Top Face. Here the algorithmic Attack to the problem is very necessary which has to uniquely specify the names of each positions of the Angle such that any user can uniquely and deterministically visualize What that position really mean and going to happen on the model.Making things with TUKKA (The Trial And Error Technic and Heuristics) is not the good thing while we need to think offline. So many times we cannot directly visualize the real top face(It comes with experience on Tekla modeling) .Until unique naming(nomenclature system) for every orientation of Parts(Specially Asymmetric Profiles like Angles) is there , we need to write so large number of if statements that even QUATERNIONS OR OCTANIONS and EULER'S THEOREMS OF SOLIDS cannot save us to automate things in pin point way.

For programmers(To handle these types of issues)

1. Unique nomenclature of position of every edge and face with specified sorting order documentation is required.

2. Unique nomenclature for positions and orientations  every irregular polygons (Irrespective of CARTESIAN GEOMETRY) is required

3. Unique pattern of formula to calculate area and perimeter of PARAMETRICALLY CLASSIFIED IRREGULAR and REGULAR POLYGON systems are required 

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Apparently looks Irrelevant but TOPOLOGICALLY Very Relevant Point is here for this post

In Structures Online(C) 

[We have sufficient large numbers of Autocad License and Advance Steel License and implemented Advance Steel effectively for many kinds of Odd shaped Structures where too much Geometric intricacies are there but Trigonometric Automation through Artificial Intelligence have solved these] 

We have started one big Endeavor under Sanjoy Nath's Geometrifying Trigonometry©  MISSION is one such endeavor which is trying to put UNIQUE NOMENCLATURE of any shaped irregular polygons(PROFILES OR CONTOUR PLATES) and to UNIQUELY ADDRESS THE TOP FACE and that will automatically decide the best fit PRE TRIANGULATION FOR PREDETERMINED STRESS PATH .With the Byproduct , we will get some more things also.We will get visualization of all kind of Trigonometric expressions to generate millions of possible pictures of arrangements of TRIANGULATIONS due to SERIES SOLUTIONS of multiple , sub multiple angles.  Large numbers of pictures are SUPPRESSED UNDER REAL 2D PLANE since Complex Numbers have BYPASSED REAL EUCLIDEAN GEOMETRY for long 370 years. STRUCTURAL ENGINEERS are not getting multiple pictures for TRUSS DESIGN just because complex numbers are SNATCHING AWAY Geometric meaningfulness of Trigonometric Expressions.

Thinking    AMBITIOUS      

We are REMOVING COMPLEX NUMBERS TO GET BACK ALL REAL GEOMETRIES HIDDEN INSIDE TRIANGLES POWER SERIES

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