Summary
We use the Gram matrix to prove that the largest number of points in R d such that the distance between all pairs is an odd integer (the square root of an odd integer) is ≤ d + 2 and we characterize all dimensions d for which the upper bound is attained. We also use the Gram matrix to obtain an upper bound for the smallest angle determined by sets of n lines through the origin in R d.
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Acknowledgements
The author is indebted to Branko Grünbaum and Victor Klee for helpful discussions during preparation of this note.
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Rosenfeld, M. (2013). In Praise of the Gram Matrix. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_35
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DOI: https://doi.org/10.1007/978-1-4614-7258-2_35
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