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A variation on the Steiner-Lehmus theme

Published online by Cambridge University Press:  22 September 2016

C. F. Parry
C. F. Parry*
Affiliation:
7 Auclum Close, Burghfield Common, Reading RG7 3DY
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Extract

A famous problem in euclidean geometry, associated with the names of J. Steiner (1796-1867) and D. C. Lehmus (1780-1863), is to show that a triangle is isosceles when two internal bisectors are equal. Although the converse is obvious, a direct proof of the statement is far from simple. A large number of demonstrations have been devised, some valid and some spurious, and a considerable literature exists on the subject.

Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 420 , June 1978 , pp. 89 - 94
Copyright
Copyright © Mathematical Association 1978 

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References

Page no 89 note † In the Gazette alone, the following contributions have been traced: 16, 200-202 (No. 219, July 1932); 17,122-126 (No. 223, May 1933); 17, 243-245 (No. 225, October 1933); 18, 120 (No. 228, May 1934), which gives a bibliography of the problem; 19, 144-145 (No. 233, May 1935); 43, 298-299 (No. 346, December 1959); 45, 214-215 (No. 353, October 1961);46,143-144(No. 356, May 1962);52,147 (No. 380, May 1968); 53,59 (No. 383, February 1969); 53,396-400 (No. 386, December 1969); 55,58 (No. 391, February 1971); 56,131 (No. 396, May 1972); 57, 336-339 (No. 402, December 1973).