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Triangles in squares*

Published online by Cambridge University Press:  01 August 2016

Liping Yuan  and
Ren Ding
Liping Yuan
Affiliation:
Department of Applied Mathematics, Hebei Normal University, Shijiazhuang 050016, People’s Republic of China e-mail: lpyuan@heinfo.net
Ren Ding
Affiliation:
Department of Applied Mathematics, Hebei Normal University, Shijiazhuang 050016, People’s Republic of China e-mail: lpyuan@heinfo.net
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Extract

In this paper we find the necessary and sufficient conditions on a, b, c, s for a triangle with sides a, b, c to fit into a square of side s.

Questions about precisely when one shape fits into another attract wide attention. In 1993 Post [1] gave necessary and sufficient conditions on the six sides of two triangles for the first to fit into the second. Recently, the necessary and sufficient conditions for squares to fit in triangles [2], equilateral triangles in triangles [3], rectangles in triangles [4] and rectangles in rectangles [5] are given. In [2] Wetzel asked when a given triangle fits into a given square. In this paper we find the necessary and sufficient conditions on a, b, c, s for a triangle with sides a, b, c to fit into a square of side s. For the sake of convenience, let α, β, γ denote the angles opposite sides a, b, c respectively, and we may assume without loss of generality that a ≥ b ≥ c, which implies that α ≥ β ≥ γ.

Type
Articles
Information
The Mathematical Gazette , Volume 88 , Issue 512 , July 2004 , pp. 219 - 225
Copyright
Copyright © The Mathematical Association 2004

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Footnotes

*

This research was supported by NSFH (199174) and NSF of Hebei Normal University.

References

1. Post, K. A., Triangle in a triangle: on a problem of Steinhaus, Geom. Dedicata 45 (1993) pp. 115–120.Google Scholar
2. Wetzel, John E., Squares in triangles, Math. Gaz. 86 (March 2002) pp. 28–34.CrossRefGoogle Scholar
3. Jerrard, R. P. and Wetzel, John E., Equilateral triangles in triangles, submitted.Google Scholar
4. Wetzel, John E., Rectangles in triangles, submitted.Google Scholar
5. Wetzel, John E., Rectangles in rectangles, Math. Mag. 73 (2000) pp. 204–211.Google Scholar