Rose Area Calculator
Compute distinct rose petals for r=a cos(kθ), integer k; odd k repeats the curve over 2π, so repeated traces are not counted as extra area.
Description
A polar rose r=a cos(kθ) has different distinct petal counts for odd and even integer k.
A polar rose r=a cos(kθ) has different distinct petal counts for odd and even integer k. Repeated tracing over a full angular cycle must not count the same petal twice.1
Compute distinct rose petals for r=a cos(kθ), integer k; odd k repeats the curve over 2π, so repeated traces are not counted as extra area.
When to use Rose Area Calculator
Use this tool to compute distinct rose petals for r=a cos(kθ), integer k; odd k repeats the curve over 2π, so repeated traces are not counted as extra area.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Rose 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 radialAmplitude, integerPetalFrequency using the field table and calculation rules, then run the tool.
- Read distinctPetalCount, onePetalArea, totalDistinctPetalArea. 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 |
|---|---|---|---|
| radialAmplitude | Radial amplitude | number | Required |
| integerPetalFrequency | Integer petal frequency | number | Required |
Use positive amplitude and integer frequency from 1 to one million. Return distinct petal count, one-petal area and their product as total distinct area in squared amplitude units.
one petal area = πa²/(4k); petals = k if odd, 2k if even Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| distinctPetalCount | Distinct petal count | number |
| onePetalArea | One petal area | number |
| totalDistinctPetalArea | Total distinct petal area | number |
{
"input": {
"radialAmplitude": 2,
"integerPetalFrequency": 3
},
"output": {
"distinctPetalCount": 3,
"onePetalArea": 1.0471975511965976,
"totalDistinctPetalArea": 3.141592653589793
}
}Limitations and assumptions
Only this integer-frequency cosine rose is modeled; general polar curves or traced multiplicity are not included.
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 Limacon Area Calculator: Compute one 0–2π polar trace area for r=a+b cos θ; when b>a inner/outer loops are both counted by polar integral, not a geometric union area. For a complementary task, use Bernoulli Lemniscate Area Calculator: Compute both-lobe and individual-lobe area for Bernoulli lemniscate r²=a² cos(2θ); scale is polar maximum radius, not focal half-distance.
References
-
Rose Area Calculator — tool.io
Similar or alternative tools
- Limacon Area Calculator
Compute one 0–2π polar trace area for r=a+b cos θ; when b>a inner/outer loops are both counted by polar integral, not a geometric union area.
- Bernoulli Lemniscate Area Calculator
Compute both-lobe and individual-lobe area for Bernoulli lemniscate r²=a² cos(2θ); scale is polar maximum radius, not focal half-distance.