Pi (π) can be calculated manually using various methods, with one notable approach being the one employed by Isaac Newton, as described in the reference.
Newton's Method for Calculating Pi Manually
The reference video details Newton's method for calculating pi. This method involves a specific formula based on square roots and arithmetic operations. Here is a step-by-step breakdown of the starting steps of the calculation:
- Initial Value: Start with the expression 3 times the square root of 3.
- First Division: Divide the result of step 1 by 4.
- First Addition: Add 24 to the result of step 2.
This process can continue with additional mathematical operations to achieve greater accuracy in the approximation of pi, which is what Newton’s method is known for.
Table Example of a few starting steps
| Step | Calculation | Result (approximate) |
|---|---|---|
| 1 | 3 * √3 | 5.196 |
| 2 | (3 * √3) / 4 | 1.299 |
| 3 | ((3 * √3) / 4) + 24 | 25.299 |
This method, while not as straightforward as using the formula directly, provides a practical and effective way to estimate pi manually. While the reference video mentioned other methods, like geometric approximations, the steps outlined above are the core starting point for Newton's approach.
