From: grossman@vela.acs.oakland.edu (Jerry Grossman)
Newsgroups: sci.math,k12.ed.math
Subject: Re: geometry problem
Date: 31 Aug 1995 12:14:30 -0400
This message is being posted by Jerry Grossman for its writer, Tony
Davie, whose system wasn't working. It's in response to the following
geometry problem that Grossman posted:
>This is a classic geometry problem, which I am embarrassed to say I can't
>see how to do. Can someone help out? A "correct" solution must use only
>elementary geometry, no trigonometry. There was an article within the
>past year on this problem and related ones, but I can't seem to find it.
>Does anyone recall where it appeared? (Other references are also
>appreciated.)
>
>ABC is a triangle. D is a point on AB, and E is a point on AC. Angle
>measures (in degrees) are as follows:
>EBC = 60 ABE = 20 BCD = 70 ACD = 10
>Find the measure of angle CDE.
This is a special case of what have become known as Adventitious angles
(or triangles or quadrangles). I have collected a small bibliography on the
subject which I show below.
If you can surf the Web, I've written a small page on the problem at
http://www.dcs.st-and.ac.uk/~ad/mathrecs/advent/advent.html
Here's the bibliography:
[lang22] A Problem: E.M. Langley, Mathematical Note 644, Mathematical
Gazette, 11, p173, 1922
[lang23] Solutions: E.M. Langley et al., Mathematical Gazette, 11,
pp321-323, 1923
[bol36] Beantwoording van prijsvraag no. 17: Nieuw Archf Wisk. (2) 18,
pp14-66, 1936
[trip75] Adventitious Angles: C.E. Tripp, Mathematical Gazette, 59,
pp98-106, 1975
[quad77] The Adventitious Angles Problem: A Progress Report: D.A. Quadling,
Mathematical Gazette, 61, pp55-58, 1977
[rigb78] Adventitious Quadrangles: J.F. Rigby, Mathematical Gazette, 62,
pp183-191, 1978
[rigb79?] Multiple Intersections of Diagonals of Regular Polygons, and
Related Topics: J.F. Rigby, Geom. Dedicata, later than [rigb78]
[quad78] Last Words on Adventitious Angles: D.A. Quadling, Mathematical
Gazette, 62, pp174-183, 1978
[mach95] Nineteen Problems on Elementary Geometry: A. Machado, Math.
Intelligencer, 17, 1, pp17-19, 1995
[gale95] Mathematical Entertainments: D. Gale, Math. Intelligencer, 17, 1,
pp21-26, 1995
[Davie's sig deleted - djr]
==============================================================================