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--- estimate_pi [2018/10/02 22:31] – created cthiel
+++ estimate_pi [2018/10/02 23:09] (current) – cthiel
@@ Line 1: / Line 1: @@
-Darts can be thrown at random points onto the square with corners (1,1) and (−1,−1). If the dart lands inside the unit circle (that is, the circle with center (0,0) and radius 1), it is a hit. Otherwise it is a miss. The proportion of hits to tries is one quarter of π.
+Start with a square and draw a circle inside with the same diameter as the square.  Darts can be thrown at random points onto this square. If the dart lands inside the circle, it counts as a hit.  The proportion of hits to tries is one quarter of π.
-Below is graphical representation.
+Below is a program that has graphical representation.
 {{ ::estimatepi.java |}}
-It takes a while to run this simulation to determine an approximate value for π.  Wright a program using a ''for'' loop or a ''while'' loop that can run 100,000 dart throws more quickly.
+[[https://mathorama.com/pisim.mov|{{:screen_shot_2018-10-02_at_7.52.17_pm.png}}]]
+It takes a while to run this simulation to determine an approximate value for π.  Write a simple text only program that uses a ''for'' loop or a ''while'' loop so that can run 200,000 dart throws more quickly the the graphical version.
+This works since the ratio of the Area of a circle divided by the Area of the square is pi*r^2 / (2r)^2 = pi/4. The ratio of the darts that land in the circle divided by the darts thrown on the square should be the same ratio, pi/4 (if we throw enough random darts!). So 4 times this proportion is pi!