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32 changes: 32 additions & 0 deletions maths/polygonal_numbers.py
Original file line number Diff line number Diff line change
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def polygonal_num(num: int, sides: int) -> int:
"""
Returns the `num`th `sides`-gonal number. It is assumed that `num` >= 0 and
`sides` >= 3 (see for reference https://en.wikipedia.org/wiki/Polygonal_number).

>>> polygonal_num(0, 3)
0
>>> polygonal_num(3, 3)
6
>>> polygonal_num(5, 4)
25
>>> polygonal_num(2, 5)
5
>>> polygonal_num(-1, 0)
Traceback (most recent call last):
...
ValueError: Invalid input: num must be >= 0 and sides must be >= 3.
>>> polygonal_num(0, 2)
Traceback (most recent call last):
...
ValueError: Invalid input: num must be >= 0 and sides must be >= 3.
"""
if num < 0 or sides < 3:
raise ValueError("Invalid input: num must be >= 0 and sides must be >= 3.")

return ((sides - 2) * num**2 - (sides - 4) * num) // 2


if __name__ == "__main__":
import doctest

doctest.testmod()