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.
Description
A hypocycloid is traced by a circle rolling inside a larger circle.
A hypocycloid is traced by a circle rolling inside a larger circle. An integer radius ratio specifies the closed curve whose enclosed area is returned.1
Exact full simple closed integer-ratio hypocycloid area; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
When to use Hypocycloid Area Calculator
Use this tool to exact full simple closed integer-ratio hypocycloid area; 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 Area 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 |
Use positive rolling radius and integer fixed/rolling ratio from 3 to one million. Return full enclosed area in squared radius units.
area = πr²(k−1)(k−2) 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": 6.283185307179586
}
}Limitations and assumptions
The formula is restricted to the declared integer-ratio simple closed curve.
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 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. For a complementary task, use Epicycloid Area Calculator: Exact full simple closed integer-ratio epicycloid area; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.
References
-
Hypocycloid Area Calculator — tool.io
Similar or alternative tools
- 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.
- Epicycloid Area Calculator
Exact full simple closed integer-ratio epicycloid area; ratio specifies cusps, not a special named-shape alias or rational-ratio multiply traced curve.