Calculate Pi by using Python simulations, following the tutorial from: junilearning
Resulting plot of approximated PI:
Imagine throwing darts on a squared dart board with a circle (radius circle = sidelength of square/2). All darts ending up in the circle are counted as "hits".
Pi can be approximated by diving the number of "hits" by the number of samples (= # darts thrown) and multiplying with factor 4.
This follows from p(hit) = hits / # darts thrown = circle area / square area = (pi * r^2) / (4 * r^2).
Therefore: 4 * # darts in circle / # darts thrown = pi
- Simulate one dart by randomly generating x and y coordinates for dart.
- Create Loop (using 1000 samples) and record data in dataframe.
- Plot results.
Table containing the sample throws:
| dart_number | hit | estimated_pi | |
|---|---|---|---|
| 0 | 1 | 1 | 4.000000 |
| 1 | 2 | 1 | 4.000000 |
| 2 | 3 | 0 | 2.666667 |
| 3 | 4 | 1 | 3.000000 |
| 4 | 5 | 1 | 3.200000 |
| ... | ... | ... | ... |
| 995 | 996 | 0 | 3.136546 |
| 996 | 997 | 1 | 3.137412 |
| 997 | 998 | 1 | 3.138277 |
| 998 | 999 | 1 | 3.139139 |
| 999 | 1000 | 1 | 3.140000 |
1000 rows × 3 columns