Circle457 2.1.0.23

Circle 45 /7 (Symmetric Arc Height Circle)

(Equal Count Symmetric Arc, Symmetric Height (1Height, 1Slope, 1Radius Translation), Circle 45 /7)

(Abstract Arc45 Circle)

This package implements Circle 45 /7 (published new circle theory ISBN: 9789999311700, https://www.elivabooks.com/pl/book/book-6489950770, https://a.co/d/0gvQNRIw).

Circle 45 /7 2D Reference:

https://www.researchgate.net/publication/381800443_Circle_457_Theory_Research_Book

Current release support following geometrical features:

1. Angle7 Circle Resolution
2. Radial Point
3. Line (or Line45, a delta height45 translation method)
4. Arc
5. Circle
6. Octet Radial Point
7. Octet Arc
8. Octet Circle

Circle 45 /7 angle resolutions are based on height method and are not same as Cosine, Sine and other similar trigonometric functions. Radius Circle 45 /7 design theory is based on equal, counts and height philosophy.

Sponsor

Download exclusive (Via Sponsor Link) research paper and data sheets that explains important concepts (Highly Recommended):

1. Width Angle Translation and Delta Height45 Line Rule (Circle457 Angle Height Concepts)
2. Circle457 Coordinate Angle Slope Resolution (Explain Quadrant and Correct Angle Resolution, Open Office Data Sheet)
3. Circle457 Graph Cycle (Proof of Symmetric Circle and Quadrant Arcs, Open Office Data Sheet)
4. Circle457 Quadrant Resolution Method (Angle Fraction Resolution, Open Office Data Sheet)
5. Circle457 Scale 1, 2.5, 5 (Circle457 Height Angles are Different and Requires New Geometrical Apparatus Scales, Open Office Data Sheet)

Disclaimer

Height (or angle height) forms the basis of a very important tool to radial resolutions and intelligent triangles. This is a new research circle drawing technology and is subject to copyright and patents. Its usage is limited to personal, educational, experimental non-commercial activities only. This software package is provided AS IS basis without any warranty or claims. This package is licensed under https://creativecommons.org/licenses/by-nc-nd/4.0/.

Research Author & Program Writer

This software package is implemented by Shams Zia research writer (author) and copyright owner of the Circle 45 /7 theory, research and publications.

Why I Should Learn Circle457

1. Its Abstract Arc45 Circle (Centralize Circle Logic Resolution to Angle 45 Arc Region), I learn Arc and I learn Circle.
2. Its Arc Height Symmetric, It Arc Count is Symmetric
3. Count Radius (Distance) of Symmetric Count (An Alternative to Pythagorean Square Root Distance Method)
4. Its Transparent, Translates Angle to Heights and Heights to Angles, Among Equal, Count, Height is an angle tool) or Height is direct angle tool. As a designer or mathematician I see angle, I see height.
5. Its Arc Translator (Height (0.707107 to Displacement (0.292893) Slope Circle), Its precise and Arc Resolution Focused
6. Heights R * 0.707107 + R * 0.292892
7. It is calculation friendly, logical or equal logical to radial counts
8. Its resolution develop equation, counting in its arcs and lines
9. Its symmetric counts claps (or coincides) with square symmetric (i.e. it count squares, resolve arcs)

Symmetric Arc Height Distance457 & Pythagorean Distance (Question of Logic)

10. Heights (or axis distance heights) along axis are directly calculated and does not require any translation. Angle heights (with diagonal distance) cannot be directly calculated and require translations. Why Pythagorean distance does not include angle as input to distance resolution when angle is translating distance?

Height Square and Pythagorean

https://doi.org/10.13140/RG.2.2.19463.15520

Solution Triangle & Distance Problem

https://doi.org/10.13140/RG.2.2.18579.03364

Perpendicular Difference

https://doi.org/10.13140/RG.2.2.28550.33604

Euclid 2D & Circle 45 /7 2D

https://doi.org/10.13140/RG.2.2.21536.34561

Other support resources: Library related support projects will be available after its release at https://github.com/shamszia/circle457.support, https://www.invincibletec.com/circle457_210/index.html.

Test Page Image:

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/12-arc45-region45-radial-4step-fine-test-data-1.png

Dated: 2026-04-25 (Version 2.1.0.1)

Add new Line45 (delta height45 difference and counting translation method), generally improves line drawing performance with difference counting method.

Dated: 2026-04-26 (Version 2.1.0.3/4)

Include origin axis radial points and line drawing.

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/20-circle45-origin-axis-radial-points-1step-fine-test-data-1.png

Dated: 2026-04-27 (Version 2.1.0.5)

Include axis scale drawing support.

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/32-axis-support-test-1.png

Dated: 2026-04-27 (Version 2.1.0.6)

Include displacing axis scale drawing support.

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/34-axis-displacement-test-1.png

Dated: 2026-04-29/30 (Version 2.1.0.7/8)

Include resolution method circle support.

Dated: 2026-05-21 (Version 2.1.0.10/11)

Introduce Slope7 angle height circle. Symmetric Height Y and Slope7 X or Symmetric Height X and Slope7 Y. Optimize with pre-calculated required angle resolution slopes and improve drawing performance.

Circle457 Research Theory Support (Version 2.1.0.10/11):

1. Symmetric Arc Height Distance Circle457 Method
2. Symmetric Arc Quadrant Height Distance Resolution Circle457 Method
3. Symmetric Arc Height X and Symmetric Arc Height Y Octet457 Method
4. Symmetric Arc Height Slope7 Circle457 Method

Origin Angle7 Coordinate Translation (Version 2.1.0.12):

1. Calculate Triangle457 (0-45) and translates angle in (0-360) degrees.
2. This version with angle7 to coordinate and coordinate to angle7 translation is drawing essential.

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/63-coordinate-translation-0-360-test1.png

Dated: 2026-05-25

Coordinate Radius (Distance) Counting (Version 2.1.0.14):

1. Introduce coordinate (radius) distance by using symmetric height7 and slope7 angle with optimized counting.

Dated: 2026-05-28

Angle Symmetric Heights Slope7 (Version 2.1.0.15/16):

1. Introduce angle symmetric heights Slope7.
2. Add symmetric heights slope arc (circle).

Dated: 2026-05-30 (Version 2.1.0.17/18):

1. Introduces coordinate (radius) distance by using midpoint perpendicular slope solution triangle, translation triangle and translated height. This is radius solution triangle design early presentation of Distance457 with assumed precision (or accumulating calculation-al decimal error of larger difference values).

Dated: 2026-05-30 (Version 2.1.0.19/20/21):

1. Introduces coordinate radial distance by calculating height difference radius.
2. Features new mathematical methods for slope7 (m7) and angle7 (a7) formulations to solve geometrical problems.

This version support 3 distance calculating methods

1. Radial Counting
2. Solution Triangle (Heights Solution)
3. Distance457 Symmetric Height Difference Method (Almost difference 0 accuracy to Pythagorean distance method).

https://github.com/shamszia/Circle457.Support/blob/main/TestsData/65-distance457-9M-tests.png

Dated: 2026-06-11 (Version 2.1.0.22):

1. Introduces angle symmetric height to height distance method (Distance457).

Dated: 2026-06-16 (Version 2.1.0.23):

1. Provide Angle7 wide distance type (DistanceType) selection for Pythagorian or Distance457.
2. General Bug Fixing.

https://github.com/shamszia/Circle457.Support