36 depicted as a triangular number and as a square number36 as the sum of the first positive cubes
36 is both thesquare ofsix, and the eighthtriangular number[1] or the sum of the first eight non-zero positiveintegers, which makes 36 the first non-trivialsquare triangular number.[2] Aside from being the smallest square triangular number other than1, it is also the only triangular number (other than 1) whosesquare root is also a triangular number. 36 is also the eighthrefactorable number, as it has exactly nine positive divisors, and9 is one of them;[3] in fact, it is the smallest positive integer with at least ninedivisors, which leads 36 to be the 7thhighly composite number.[4] It is the sum of the fourth pair oftwin-primes (17 +19),[5] and the 18thHarshad number indecimal, as it is divisible by the sum of its digits (9).[6]
Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is anErdős–Woods number.[11]
Jewish tradition holds that the number 36 has had special significance since the beginning of time: According to theMidrash, the light created byGod on the first day ofcreation shone for exactly 36 hours; it was replaced by the light of theSun that was created on the Fourth Day.[15] TheTorah commands 36 times to love, respect and protect the stranger.[15] Furthermore, in every generation there are 36righteous people (the"Lamed Vav Tzadikim") in whose merit the world continues to exist.[15] In the modern celebration ofHanukkah, 36 candles are kindled in themenorah over the eight days of that holiday (not including theshamash candle).[15]
