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  • 1 UNAM Instituto de Matemáticas Ciudad de México Mexico
  • 2 Universidad Autónoma de Guerrero Facultad de Matemáticas Guerrero Mexico
  • 3 UNAM Instituto de Matemáticas Cuernavaca Mexico
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Abstract  

In this paper the following is proved: letK ∈ ℝ2be a convex body and t ∈ [0, 1/4]. If the diameter of K is at least √37 times the minimum width, then there is a pair of orthogonal lines that partition K into four pieces of areas t, t, (1/2−t), (1/2−t) in clockwise order. Furthermore, if K is centrally symmetric, then we can replace the factor √37 by 3.