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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

Topic: equilateral triangle
Replies: 13   Last Post: Jan 8, 2002 4:18 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: equilateral triangle (Spoiler)
Posted: Jan 8, 2002 4:18 PM
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On 23 Nov 2001, Rouben Rostamian wrote:

> Dan Hoey <haoyuep@aol.com> proved that:
>
> Let ABC be an equilateral triangle and let P be an arbitrary
> point anywhere in the plane of ABC. Then PC <= PA + PB.
>
> [Proof omitted]
>
> Dan, that's a wonderful proof. Much neater than I could have
> imagined. It ought to become a classic. Congratulations!

It suggests a number of questions. For starters, what's the set of
shapes for ABC that still yield this (a): one way round, and (b):
all three ways round (so that PA,PB,PC can be used as triangle edges)?

John Conway

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