Calculator Input
Spiral Graph
Example Data Table
| Step | Hypotenuse | Angle | Triangle Area |
|---|---|---|---|
| 1 | 10 cm | 45° | 50 cm2 |
| 2 | 14.14 cm | 35.26° | 50 cm2 |
| 3 | 17.32 cm | 30° | 70.71 cm2 |
| 4 | 20 cm | 26.57° | 86.6 cm2 |
| 5 | 22.36 cm | 24.09° | 100 cm2 |
| 6 | 24.49 cm | 22.21° | 111.8 cm2 |
| 7 | 26.46 cm | 20.7° | 122.47 cm2 |
| 8 | 28.28 cm | 19.47° | 132.29 cm2 |
| 9 | 30 cm | 18.43° | 141.42 cm2 |
| 10 | 31.62 cm | 17.55° | 150 cm2 |
| 11 | 33.17 cm | 16.78° | 158.11 cm2 |
| 12 | 34.64 cm | 16.1° | 165.83 cm2 |
Formula Used
The Pythagorean spiral uses right triangles joined one by one.
Radius at step n: r = a√n
Angle added: θ = tan-1(a / r)
Triangle area: A = 1/2 × base × height
Here, a is the starting side length. For a 10cm base, step 10 gives 10√10 cm.
How to Use This Calculator
- Enter the base side length, such as 10 cm.
- Choose the number of spiral steps.
- Select decimal precision.
- Press the calculate button.
- Review radius, angle, area, graph, and table.
- Download CSV or PDF for records.
About Pythagorean Spiral 10cm Calculations
A Pythagorean spiral is also called the spiral of Theodorus. It is built from connected right triangles. Each new triangle uses one fixed side and the previous hypotenuse. This creates a smooth growing spiral. A 10cm version means the fixed triangle leg is 10cm. The first hypotenuse becomes 10√1. The second becomes 10√2. The third becomes 10√3. This pattern continues clearly.
This calculator helps students, teachers, designers, and geometry learners. It removes repeated manual square root work. It also provides angle estimates for each step. These angles help when drawing the spiral on paper. They are useful for classroom boards, craft layouts, and technical diagrams. The area column gives another useful comparison. It shows how each triangle contributes to the growing shape.
The graph gives a fast visual check. You can see how radius increases with each step. The growth is not linear. It follows a square root pattern. That means each new radius still grows. Yet the added length becomes smaller compared with earlier jumps. This is why the spiral expands gradually.
Use clean measurements when drawing. Keep the fixed side constant. Draw every right angle carefully. Small angle errors can affect later points. For accurate construction, use a ruler, compass, and protractor. This tool gives the numerical plan before drawing. It also exports results for worksheets, reports, and project files.
FAQs
What is a Pythagorean spiral?
It is a spiral made from connected right triangles. Each triangle uses a fixed side and the previous hypotenuse.
Why use 10cm?
Ten centimeters is easy to measure. It also makes square root lengths simple to scale and compare.
What does step number mean?
The step number represents each triangle added to the spiral. Higher steps show larger radius values.
What is the main formula?
The main formula is r = a√n. Here, a is side length, and n is the spiral step.
Can I change the base length?
Yes. Enter any positive side length. The calculator updates radius, angle, area, table, and graph.
Is this useful for drawing?
Yes. It gives lengths and angles that help you draw each triangle more accurately.
Does the spiral grow evenly?
No. The radius follows square root growth. It increases, but each relative jump becomes smaller.
Can I export my results?
Yes. You can download a CSV file or a PDF summary directly from the result section.