Rose curve petal counter
Enter the coefficient k of a polar rose and get its petal count: k equal to 3 gives 3 petals, while k equal to 4 gives 8, because even values double the loops. The amplitude never matters. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- K
- 3
- Petals
- 3
- Parity
- odd
- Polar
- r = a·sin(kθ) or r = a·cos(kθ)
Polar rose curves—also called rhodonea curves—appear in precalculus, calculus polar units, graphics demos, and exam problems that ask how many petals the graph of r equals a times sin of k theta (or cos of k theta) will show. Students often confuse the odd and even cases, counting k petals when the book expects 2k, or the reverse. This rose curve petal counter accepts the angular coefficient k, validates that k is a positive integer, and returns the classical petal count together with parity and a short formula string you can show beside a plot. Odd positive integers produce k distinct petals; even positive integers produce 2k petals because the curve completes a full double cover of the angular period. Amplitude a never changes the count, so only k is required.
What a rose curve is and why petal count depends on k
A rose curve in the polar plane is the graph of r equals a times sin of k theta, or r equals a times cos of k theta, where a is a non-zero amplitude and k is a positive constant that scales the angle. When k is a positive integer the graph forms a finite number of loops that look like flower petals arranged around the origin.
The geometric reason the count splits on parity is period and overlap: for odd k the polar equation completes its distinct petal set once the angle runs through an interval of length pi, so you see exactly k petals; for even k the sine or cosine factor has an extra sign symmetry that only fully unfolds over a full 0 to 2pi sweep, doubling the number of loops to 2k.
Classic textbook examples make this concrete: k equals three yields a three-petal rose; k equals four yields an eight-petal rose; k equals five yields five petals; k equals two yields four petals. Cosine roses are rotated copies of the corresponding sine roses for the same integer k; they share the same petal count. Fractional or irrational k produce more exotic dense windings that are outside the classical petal-count rule this capability implements.
What you enter and what you get back
On success the body echoes k, reports petals as the integer petal count, sets parity to the string odd or even, and includes formula and polar strings that restate the classical rule and the polar forms r equals a sin k theta or a cos k theta. Example: k equals three returns petals three, parity odd, and the formula k odd implies petals equals k. Example: k equals four returns petals eight, parity even, and the formula k even implies petals equals 2k.
The capability does not plot the curve, does not require amplitude a, and does not distinguish sin from cos for counting purposes.
Where counting rose petals helps
Classrooms and tutoring platforms use a rose curve petal counter so learners can check odd versus even cases without memorising the rule incorrectly. Exam generators and LMS plugins need a deterministic oracle that marks k equals four as eight petals and rejects non-integer k instead of silently returning a plausible but wrong number. Creative-coding and generative-art notebooks often parameterise rhodonea motifs by k and want a quick validation step before sampling points for a canvas or SVG.
Failed validation does not consume balance. Keep requests small, pin the integer petals field in tests, and you get reproducible counts for homework, LMS plugins, and edge workers without standing up a full computer-algebra or plotting stack just to answer how many petals a rose has.
What you can do with it
Classroom and homework checks
Let students submit integer k for r=a·sin(kθ) or cos and verify the odd-k versus even-k petal count against textbook answers.
Exam and LMS auto-grading
Mark rose-curve items with a deterministic oracle that returns k or 2k correctly and rejects non-positive or non-integer k.
Generative art and polar demos
Validate petal counts for rhodonea parameters before sampling polar points in canvas, SVG, or notebook visualisations.
FAQ
How many petals does a rose curve with coefficient k have?
For positive integer k: if k is odd the rose has k petals; if k is even it has 2k petals.
Does sin(kθ) versus cos(kθ) change the petal count?
No. For the same positive integer k, sine and cosine roses are rotated copies of each other and share the same petal count.
What happens if k is not a positive integer?
Fractions, zero, negatives, and non-finite values are rejected and are not billed.
Do I need to send the amplitude a?
No. Amplitude scales the size of the petals but does not change how many petals appear. Only k is required.
Why does an even k give twice as many petals?
With an odd k, the curve draws its whole set of petals while the angle runs through pi, half a turn. With an even k, an extra sign symmetry only unfolds over the full turn, so the loops double to 2k.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/geom/rose-curve-petals \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"k":3}'const res = await fetch("https://api.kit.forhosting.com/geom/rose-curve-petals", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"k": 3
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/rose-curve-petals",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"k": 3
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/rose-curve-petals", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"k":3}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"k":3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/rose-curve-petals", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"k": 3
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.rose_curve_petals",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
The same pure logic powers the free browser path and the API path, so homework checks and automation never disagree on a textbook edge case.
What a rose curve is and why petal count depends on k
The endpoint therefore insists that k be a positive integer and refuses any other value rather than inventing a continuous generalisation that textbooks do not teach under the name petal count.
Input contract, response fields, and error behaviour
POST a JSON body with one required field: k, the angular coefficient. k may arrive as a JSON number or as a numeric string; it must be a finite positive integer greater than or equal to one. Missing k, empty strings, non-finite values, fractions such as 2.5, zero, and negative integers all fail with invalid_input and a message that names the rule that was broken. Those validation failures are not billed. Pair the numeric result with your own graphing library if you need a sketch; use this endpoint when the only question is how many petals the integer-k rose has.
Technical questions
What does the rose curve petal counter cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.