Added Madhava-Leibniz infinite sum

Yonaba · Yonaba · commit f4faddbcccf3 · 2014-04-09T21:11:54.000Z
diff --git a/Pi_Algorithms/Lua/Yonaba/pi.lua b/Pi_Algorithms/Lua/Yonaba/pi.lua
@@ -3,6 +3,7 @@
 
 -- Evaluates Pi using a random and statistical approach
 --   (Monte-Carlo method) to evaluate pi
+-- See: http://en.wikipedia.org/wiki/Pi#Geometry_and_trigonometry
 -- n      : the number of simulations (should be high)
 -- seed   : (optional) a custom seed to init the RNG
 -- returns: an approximation of pi
@@ -17,3 +18,16 @@ local function statistical_pi(n, seed)
   end 
   return 4 * (count / n)
 end
+
+-- Evaluates Pi using Madhava-Leibniz infinite series
+-- See: http://en.wikipedia.org/wiki/Pi#Infinite_series
+-- n      : (optional) the order of the infinite sequence to reach (defaults to 100)
+-- returns: an approximation of pi
+local function madhava_leibniz_series(n)
+  local k, sum = 0, 0
+  n = n or 100
+  for k = 0, n do
+    sum = sum + ((-3)^(-k)) / (2 * k + 1)
+  end
+  return math.sqrt(12) * sum
+end
