Angles & Circular Arithmetic
SkillDev toolsAbstract math for angle measurement, unit systems, and circular arithmetic. USE FOR: implementing angle types; converting between degrees/radians/gradians/revolutions; reducing angles to canonical range [0, Full); computing reference angles and quadrants; implementing safe modular arithmetic with negative inputs; angle addition and subtraction; classifying angles by sign and size. DO NOT USE FOR: trigonometric functions (use trigonometric-functions); coordinate conversions (use coordinate-system-conversions); interpolation (use interpolation-on-manifolds).
Available today. Use it from your connected AI after setup.
No other account needed.
Connect ahel once, and every AI you use reads what you have installed.
Then ask your AI: use the Angles & Circular Arithmetic skill
What this skill tells your AI
The instructions your AI receives, as published by netfabric/netfabric.numerics in .agents/skills/angles-and-circular-arithmetic/SKILL.md and read by ahel’s review.
Unit Systems
| Unit | Full (2π equiv) | Right | Straight |
|---|---|---|---|
| Degrees | 360 | 90 | 180 |
| Radians | 2π | π/2 | π |
| Gradians | 400 | 100 | 200 |
| Revolutions | 1 | 0.25 | 0.5 |
Conversion Factors (multiply source by factor)
| From \ To | Degrees | Radians | Gradians | Revolutions |
|---|---|---|---|---|
| Degrees | 1 | π/180 | 10/9 | 1/360 |
| Radians | 180/π | 1 | 200/π | 1/(2π) |
| Gradians | 9/10 | π/200 | 1 | 1/400 |
| Revolutions | 360 | 2π | 400 | 1 |
Canonical Reduction to [0, Full)
reduced = θ − Full × ⌊θ / Full⌋
| Input (degrees) | Result |
|---|---|
| −30° | 330° |
| 0° | 0° |
| 360° | 0° |
| 720° | 0° |
| −360° | 0° |
Quadrant Classification (after reduction to [0°, 360°))
| Range | Name |
|---|---|
| θ = 0° | PositiveX axis |
| 0° < θ < 90° | First |
| θ = 90° | PositiveY axis |
| 90° < θ < 180° | Second |
| θ = 180° | NegativeX axis |
| 180° < θ < 270° | Third |
| θ = 270° | NegativeY axis |
| 270° < θ < 360° | Fourth |
Reference Angle (acute angle to nearest x-axis)
| Quadrant | Formula |
|---|---|
| First | θ |
| Second | 180° − θ |
| Third | θ − 180° |
| Fourth | 360° − θ |
Reference Files
| File | Load When |
|---|---|
| references/formulas.md | Unit conversion derivations, reduction algorithm, DMS format, arithmetic proofs |
| references/numerical-stability.md | Mod with negatives, precision loss in conversion, large-angle reduction |
Signals
- GitHub stars
- 36
- Forks
- 1
- Last commit
- Aug 2026
Advanced
- Catalog kind
- skill
- Gateway key
angles-and-circular-arithmetic- Source
- github.com/netfabric/netfabric.numerics