From 212a1e13e5409ef81fbf4d2d525e5e4a1a01e0eb Mon Sep 17 00:00:00 2001 From: Stephen Seo Date: Wed, 18 Aug 2021 19:26:56 +0900 Subject: [PATCH] Add problem --- problem | 39 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 39 insertions(+) create mode 100644 problem diff --git a/problem b/problem new file mode 100644 index 0000000..e630a0f --- /dev/null +++ b/problem @@ -0,0 +1,39 @@ +In mathematics, the arithmetic geometric mean of two positive real numbers is +computed by repeatedly taking half their sum and the square root of their +product until the two numbers converge. For instance, the arithmetic geometric +mean of 24 and 6 is 13.456171…, with the iterative steps computed as follows: + +0 24 6 +1 15 12 +2 13.5 13.416407864998738175455042 +3 13.458203932499369089227521 13.458139030990984877207090 +4 13.458171481745176983217305 13.458171481706053858316334 +5 13.458171481725615420766820 13.458171481725615420766806 + +The arithmetic geometric mean was invented by Lagrange and studied by Gauss, and +is used today to compute various transcendental functions because it converges +so quickly. + +In the world of Randall Munroe, the geothmetic meandian of any set of positive +numbers is computed by iterating three sequences — the arithmetic mean, the +geometric mean, and the median — until they converge. For instance, the +geothmetic meandian of the set (1,1,2,3,5) is 2.089, computed as follows: + +1 2.4 1.9743504858348200 2 +2 2.1247834952782734 2.1161924605448084 2 +3 2.0803253186076938 2.0795368194795802 2.1161924605448084 +4 2.0920181995440275 2.0919486049152223 2.0803253186076938 +5 2.0880973743556477 2.0880901331209600 2.0919486049152223 +6 2.0893787041306098 2.0893779142184865 2.0880973743556477 +7 2.0889513309015815 2.0889512436159920 2.0893779142184865 +8 2.0890934962453533 2.0890934865653277 2.0889513309015815 +9 2.0890461045707540 2.0890461034958396 2.0890934865653277 + +[ I hate the damned new editor at WordPress; I struggle with it every time I +post an exercise. I could not figure out how to embed the image from XKCD in +this blog post. You can see it here. ] + +Your task is to write programs that compute the arithmetic geometric mean and +geothmetic meandian. When you are finished, you are welcome to read or run a +suggested solution, or to post your own solution or discuss the exercise in the +comments below.