magnitude at 10100. accurate to eleven digits: accurate to twelve digits: accurate to 16 digits: - inverse of sum of first two terms of Ramanujan series. accurate to 18 digits: This is based on the fundamental discriminant = 3(89) = 267 which has class number (-) = 2 explaining the algebraic numbers of degree 2. The core radical is 53 more than the fundamental unit which gives the smallest solution { , } = {500, 53} to the Pell equation 2 − 892 = −1. accurate to 24 digits: - inverse of sum of first three terms of Ramanujan series. accurate to 30 decimal places: Derived from the closeness of Ramanujan constant to the integer 6403203+744. This does not admit obvious generalizations in the integers, because there are only finitely many Heegner numbers and negative discriminants d with class number h(−d) = 1, and d = 163 is the largest one in absolute value. accurate to 52 decimal places: Like the one above, a consequence of the j-invariant. Among negative discriminants with class number 2, this d the largest in absolute value. accurate to 161 decimal places: where u is a product of four simple quartic units, and, Based on one found by Daniel Shanks. Similar to the previous two, but this time is a quotient of a modular form, namely the Dedekind eta function, and where the argument involves . The discriminant d = 3502 has h(−d) = 16. The continued fraction representation of can be used to generate successive best rational approximations. These approximations are the best possible rational approximations of relative to the size of their denominators. Here is a list of the first thirteen of these: Of these, is the only fraction in this sequence that gives more exact digits of (i.e. 7) than the number of digits needed to approximate it (i.e. 6). The accuracy can be improved by using other fractions with larger numerators and denominators, but, for most such fractions, more digits are required in the approximation than correct significant figures achieved in the result. Summing a circle's area Pi can be obtained from a circle if its radius and area are known using the relationship: If a circle with radius is drawn with its center at the point (0, 0), any point whose distance from the origin is less than will fall inside the circle. The Pythagorean theorem gives the distance from