Counting Angles and Rays
Date: Wed, 23 Aug 1995 23:21:22 -0400 From: Anonymous Subject: Angles and rays My daughter asked me for help with this problem. What is the algebraic expression to show the relation of the number of angles created as rays are added from a common point? For example--two rays create one angle three rays create three angles four rays create six angles Is there a formula to know how many angles are created from 37 rays from a common point?? Thanks in advance
Date: 8/23/95 at 23:34:10 From: Doctor Ken Subject: Re: Angles and rays Hello! To do this problem, you have to ask yourself "what is it that is really defining the angle here?" The angle is being defined by two of the rays coming from the common point. So to figure out how many angles are being formed, you have to figure out how many ways you can choose two objects from a collection of 37 objects, when order isn't important. Well, it just so happens that there's a really handy formula that can tell us exactly that. It's called the "choose" formula. It says that the number of ways of choosing p objects from a collection of n objects, when order doesn't matter (choosing one then another is the same as choosing them in the reverse order) is n!/(p!(n-p)!). I'll write it here as C[n,p]. So in our case, we're choosing 2 rays from a collection of n rays, so our formula becomes n!/(2(n-2)!) = n(n-1)/2. In the case of 37 rays, that's 666 (ooh) rays. -Doctor Ken, The Geometry Forum
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