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math.MG2019
Diamond Twin
Toshikazu Sunada
As noticed in 2006 by the author of the present article, the hypothetical crystal---described by crystallographer F. Laves (1932) for the first time and designated ``Laves' graph o…
math.HO2019
From Euclid to Riemann and Beyond
Toshikazu Sunada
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More s…