Description
Require sides 3-1000000 and return cos(π/sides).
Polygon formulas combine edge, angle, and area contributions under a stated shape model. A single shoelace term or turning-angle ratio is only part of a full polygon computation and does not independently validate its boundary.
Require sides 3-1000000 and return cos(π/sides).
When to use this tool
Use Regular Polygon Apothem Radius Ratio when you need a polygon dimension, angle, or local accumulation term.
How to use the tool and how it works
- Enter sides. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio. Use the output convention below.
Require sides 3-1000000 and return cos(π/sides).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sides | Sides | Required. Safe integer; minimum 3; maximum 1000000. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Dimensionless ratio under the numerator/denominator convention above. | Required. Finite number. |
{
"input": {
"sides": 3
},
"output": {
"ratio": 0.5000000000000001
}
}Limitations and assumptions
- The ratio is apothem divided by circumradius for a regular polygon; no dimensions or actual polygon are validated and the output is dimensionless.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Evaluate the complete ordered boundary for area, winding, and validity. Use a general polygon method when regularity, simplicity, convexity, or uniform shape assumptions do not hold.
References
Similar or alternative tools
- Regular Polygon Central Angle Halfangle Pair
Return 2π/sides for centralRadians and π/sides for halfRadians.
- Regular Polygon Side Sagitta
Return 2 × radius × sin(π/(2 × sides))² as sagitta.