In each of the following select a digit 0,1,...,9 so that the statement or formula is correct. Each digit should occur exactly once.
A) Definition: For any circle, A × π =
B) In I Kings 7:23 (circa 950 BC) the value B appears to be used for π.
(Not so erroneous depending on ones interpretation.)
C) Earlier the Babylonians (1900-1680 BC) had used the ratio 2C/8 as a better approximation to π.
D) The Egyptians in the Rhine Papyrus (circa 1650 BC) used
as an approximation to π. E) In the year 189E, the Indiana House of Representatives passed a bill (#246) patenting such approximations to π with the intent of charging other states for its use. (Fortunately the bill never made it though the senate thanks to the presence of a math professor and π remains in the public domain.)
F) De Moivre (1667-1754) found the elegant formula
+ 1 = F which relates π, the imaginary unit, the natural log base and the additive and multiplicative identities.G)
The following infinite series have been used to approximate π.
H) 1 -
+ 
- 
+ 
- 
+ ... = 
(Gregory & Leibnitz, 17th century)I) 1 +
+ 
+ 
+ 
+ ... = 
(Euler, 1735)J)
=
(Ramanujan, 1909)Series such as Ramaujan's in which each term appears complicated but for which the convergence is rapid have enabled pi to be computed to more than one billion places.
