birthdates.py

# average birthdates of the presidents

birthdates = [
    (1732,  2, 22),     # Washington
    (1735, 10, 30),     # Adams
    (1743,  4, 13),     # Jefferson
    (1751,  3, 16),     # Madison
    (1758,  4, 28),     # Monroe
    (1767,  7, 11),     # Adams (JQ)
    (1767,  3, 15),     # Jackson
    (1782, 12,  5),     # Van Buren
    (1773,  2,  9),     # Harrison (WH)
    (1790,  3, 29),     # Tyler
    (1795, 11,  2),     # Polk
    (1784, 11, 24),     # Taylor
    (1800,  1,  7),     # Fillmore
    (1804, 11, 23),     # Pierce
    (1791,  4, 23),     # Buchanan
    (1809,  2, 12),     # Lincoln
    (1808, 12, 29),     # Johnson (A)
    (1822,  4, 27),     # Grant
    (1822, 10,  4),     # Hayes
    (1831, 11, 19),     # Garfield
    (1829, 10,  5),     # Arthur
    (1837,  3, 18),     # Cleveland
    (1833,  8, 20),     # Harrison
    (1843,  1, 29),     # McKinley
    (1858, 10, 27),     # Roosevelt (T)
    (1857,  9, 15),     # Taft
    (1856, 12, 28),     # Wilson
    (1865, 11,  2),     # Harding
    (1872,  7,  4),     # Coolidge
    (1874,  8, 10),     # Hoover
    (1882,  1, 30),     # Roosevelt (FD)
    (1884,  4,  8),     # Truman
    (1890, 10, 14),     # Eisenhower
    (1917,  5, 29),     # Kennedy
    (1908,  8, 27),     # Johnson (LB)
    (1913,  1,  9),     # Nixon
    (1913,  7, 14),     # Ford
    (1924, 10,  1),     # Carter
    (1911,  2,  6),     # Reagan
    (1924,  6, 12),     # Bush (GHW)
    (1946,  8, 19),     # Clinton
    (1946,  7,  6),     # Bush (GW)
    (1961,  8,  4),     # Obama
    (1946,  6, 14)      # Trump
    ]

from datetime import date
from math import sin, cos, pi, atan2

sum_x = sum_y = 0

def isleap(year):
    "Return True if the given year is a leap year in the Gregorian calendar."
    if year % 4 != 0: return False
    if year % 100 != 0: return True
    if year % 400 != 0: return False
    return True

# For each birthdate:
for datetuple in birthdates:
    birthdate = date(*datetuple).timetuple()

    # Get the day of the year.
    birthdate_of_year = birthdate.tm_yday

    # Account for leap years.
    yeardays = 366.0 if isleap(birthdate.tm_year) else 365.0

    # Turn the day of the year into an angle between 0 and 2pi.
    angle = (float(birthdate_of_year) / yeardays) * 2 * pi

    # Sum up the components separately.
    sum_y += sin(angle)
    sum_x += cos(angle)

# Average the components and convert back to a number between 1 and 365.
sum_y /= len(birthdates)
sum_x /= len(birthdates)
average_dayofyear = ((atan2(sum_y, sum_x) / (2 * pi)) * 365) + 1
if average_dayofyear < 0:
    average_dayofyear += 365

print(average_dayofyear)
# Prints: 345.9946101235643
# "December 12 is the 346th day of the year (347th in leap years) in the Gregorian calendar."