36 (number) 36 (number) 36 (thirty-six) is the natural number following 35 and preceding 37. 36 is both the square of six and a triangular number, making it a square triangular number. It is the smallest square triangular number other than one, and it is also the only triangular number other than one whose square root is also a triangular number. It is also a circular number- a square number that ends with the same integer by itself (6×6=36). It is the smallest number "n" with exactly eight solutions to the equation φ("x") = "n". Being the smallest number with exactly nine
Square root of 2 The number can also be expressed by taking the Taylor series of a trigonometric function. For example, the series for gives The Taylor series of with and using the double factorial gives The convergence of this series can be accelerated with an Euler transform, producing It is not known whether can be represented with a BBP-type formula. BBP-type formulas are known for and , however. The number can be represented by an infinite series of Egyptian fractions, with denominators defined by 2th terms of a Fibonacci-like recurrence relation a(n)=34a(n-1)-a(n-2), a(0)=0, a(1)=6. The square root of two has the following continued