Re: United Airlines magazine has surprisingly hard geometry problem

From: David Bernier (david250_at_videotron.ca)
Date: 07/29/04 

Date: Wed, 28 Jul 2004 22:58:20 -0400

Bart Goddard wrote:
> wrote:
>
>
>>In article <40fd290f$0$563$b45e6eb0@senator-bedfellow.mit.edu>, I
>>wrote:
>>
>>> Let ABC be a triangle with a point D on side AB and a point E on
>>> side AC. We are given the following angles (in degrees):
>>>
>>> ABE = 20; EBC = 60; ACD = 10; DCB = 70.
>>>
>>> Problem: What is angle CDE in degrees?
>>>
>>>One can brute-force this with a lot of trigonometry, but what's the
>>>slick solution? Someone I showed this to said that he'd seen this
>>>problem before but unfortunately he couldn't remember the reference.
>>
>>Matthew Frank found a reference: "Geometry Civilized" by Heilbron.
>>It's the last problem in the book and is dubbed "The Tantalus
>>Problem." The solution given is, in my opinion, less elegant than
>>Hiraga's. The book mentions that this problem appeared in the
>>Washington Post in 1995 and generated quite a buzz at that time.
>
>
> I showed the problem to a visiting Hungarian geometer (Ferenc Fodor)
> here at U of Calgary (where I am also visiting.) He immediately
> recognized the problem as "classic" and said that there was some
> anecdote about von Neumann solving it. But Google hasn't yielded
> anything like that for me. That would make the problem at least
> 50 years old, anyway.

I saw David Rusin's recent re-post. With respect to the original
problem and references, you might want to look at a bibliography
on "adventitious angle" problems compiled by Tony Davie which
appears on David Rusin's _Mathematical Atlas_ Web site
at the following URL:

    http://www.math-atlas.org/95/adventitious

The earliest reference given is to a 1922 Note by E.M. Langley
that appeared in The Mathematical Gazette. I'd be curious to
know what was in that 1922 Note....

David Bernier

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