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September 17, 2024 02:43
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|a[n] - a[m]| / |n - m| = r
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| #!/usr/bin/env python3 | |
| import sys | |
| def main(): | |
| """ | |
| Demonstração de que dado uma P.A. com razão constante, existe uma proporção | |
| entre a diferença entre os índices de 2 termos quaisquer e a diferença de | |
| seus valores. | |
| Ou seja, esse script demonstra que: | |
| |a[n] - a[m]| / |n - m| = r | |
| Exemplo: | |
| P.A.: 3, 6, 9, 12, 15, 17 ... | |
| r = 3 | |
| |a3 - a5| / |3 - 5| = 3 | |
| """ | |
| if len(sys.argv) < 3: | |
| print("Usage: ./pa-demo.py <a1> <r> [nvalues]") | |
| exit(0) | |
| a1 = int(sys.argv[1]) | |
| r = int(sys.argv[2]) | |
| nvalues = 10 if len(sys.argv) <= 3 else int(sys.argv[3]) | |
| first_values = [a1 + i*r for i in range(nvalues)] | |
| print(f"First {nvalues} values:", first_values) | |
| for ix, x in enumerate(first_values): | |
| for iy, y in enumerate(first_values): | |
| if ix == iy: | |
| continue | |
| calculated_r = abs(x - y) / abs(ix - iy) | |
| print( | |
| f"|{x} - {y}| / |{ix + 1} - {iy + 1}| =", | |
| calculated_r, | |
| ) | |
| if calculated_r != r: | |
| print(f"ERROR! {calculated_r} is not equal to {r}") | |
| exit(1) | |
| if __name__ == '__main__': | |
| main() |
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