Hypocycloid Perimeter Calculator
Exact full simple closed integer-ratio hypocycloid perimeter; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
Description
An integer-radius-ratio hypocycloid closes after one simple full curve.
An integer-radius-ratio hypocycloid closes after one simple full curve. The ratio determines its cusp count and must match the geometric convention.1
Exact full simple closed integer-ratio hypocycloid perimeter; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
When to use Hypocycloid Perimeter Calculator
Use this tool to exact full simple closed integer-ratio hypocycloid perimeter; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Hypocycloid Perimeter Calculator and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter rollingRadius, fixedToRollingRadiusIntegerRatio using the field table and calculation rules, then run the tool.
- Read curveMeasure. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| rollingRadius | Rolling radius | number | Required |
| fixedToRollingRadiusIntegerRatio | Fixed to rolling radius integer ratio | number | Required |
Enter positive rolling radius r and integer fixed-to-rolling radius ratio k from 3 to one million. Compute the complete curve length in radius units.
perimeter = 8r(k−1) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| curveMeasure | Curve measure | number |
{
"input": {
"rollingRadius": 1,
"fixedToRollingRadiusIntegerRatio": 3
},
"output": {
"curveMeasure": 16
}
}Limitations and assumptions
Rational noninteger ratios and multiply traced trajectories are excluded.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Hypocycloid Area Calculator: Exact full simple closed integer-ratio hypocycloid area; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve. For a complementary task, use Epicycloid Perimeter Calculator: Exact full simple closed integer-ratio epicycloid perimeter; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
References
-
Hypocycloid Perimeter Calculator — tool.io
Similar or alternative tools
- Hypocycloid Area Calculator
Exact full simple closed integer-ratio hypocycloid area; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
- Epicycloid Perimeter Calculator
Exact full simple closed integer-ratio epicycloid perimeter; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.