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Wednesday, 09 May 2012 13:22

A puzzle for the mathematically minded

By

I'd like to start a series of puzzles for our readers. Some will require cunning and insight, others sheer brain power. The first one (below) is definitely in the latter category.

I'll give you the "cute scenario" first, then rephrase as a more strict mathematical puzzle later on.

Imagine a perfectly circular paddock in which a grazing animal is tied to the edge. The question is simple - how long should the rope be such that the animal can eat exactly half of the grass in the paddock.

For the more mathematically minded, define a circle or radius r1. What is the radius of a second circle r2, the centre of which is positioned on the circumference of the first circle and the area of intersection of the two circles is exactly half the total area of the first circle (diagram below).

By preference, the value of r2 should be expressed as a proportion of r1. Even greater kudos for whoever can express the result in terms of circle-friendly operators (for instance, something like, r2 = 4/3 π r1 [hint - this is NOT even remotely the correct answer, merely a descriptor of the framework of the preferred answer]).

Answers in the comments please.

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David Heath

David Heath has had a long and varied career in the IT industry having worked as a Pre-sales Network Engineer (remember Novell NetWare?), General Manager of IT&T for the TV Shopping Network, as a Technical manager in the Biometrics industry, and as a Technical Trainer and Instructional Designer in the industrial control sector. In all aspects, security has been a driving focus. Throughout his career, David has sought to inform and educate people and has done that through his writings and in more formal educational environments.

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