TY - JOUR
T1 - The three gap theorem and the space of lattices
AU - Marklof, Jens
AU - Strombergsson, Andreas
PY - 2017/10
Y1 - 2017/10
N2 - The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence α, 2α, ⋯, Nα, for any integer N and real number α. This statement was proved in the 1950s independently by various authors. Here we present a different approach using the space of two-dimensional Euclidean lattices.
AB - The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence α, 2α, ⋯, Nα, for any integer N and real number α. This statement was proved in the 1950s independently by various authors. Here we present a different approach using the space of two-dimensional Euclidean lattices.
UR - http://www.scopus.com/inward/record.url?scp=85032619352&partnerID=8YFLogxK
U2 - 10.4169/amer.math.monthly.124.8.741
DO - 10.4169/amer.math.monthly.124.8.741
M3 - Article (Academic Journal)
AN - SCOPUS:85032619352
SN - 0002-9890
VL - 124
SP - 741
EP - 745
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 8
ER -