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A simple proof of the Beijing theorem

Published online by Cambridge University Press:  01 August 2016

Michael A.B. Deakin
Michael A.B. Deakin*
Affiliation:
Dept. of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Extract

If a square pyramid is cut obliquely by a plane as shown in figure 1, a pentagonal cross-section PQSTR is generated. The “Beijing theorem”states that the only case in which this pentagon can be regular is that in which the pyramid is half an octahedron and (except for a complication to be discussed later) the coordinates of the points P, Q, R, S and T are uniquely determined.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 76 , Issue 476 , July 1992 , pp. 251 - 254
Copyright
Copyright © The Mathematical Association 1992

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References

1. Chou, S.-C., “A collection of geometry theorems proved mechanically”, Inst. Comp. Sei. Tech. Rep. 50 (1986), U. of Texas at Austin.Google Scholar
2. Deakin, M.A.B., “A computer-generated theorem in elementary geometry”. Function 15 (1991) 8–12.Google Scholar
3. Mcintosh, C.B.G., Letter to the editor, ibid. 48–50.Google Scholar