The notion of orthogonality for vectors in inner product spaces is simple,
interesting and fruitful. When moving to normed spaces, we have many
possibilities to extend this notion. We consider Birkhoff orthogonality and
isosceles orthogonality, which are the most used notions of orthogonality.
In 2006, Ji and Wu introduced a geometric constant D(X) to give a
quantitative characterization of the difference between these two
orthogonality types. However, this constant was considered only in the unit
sphere SX of the normed space X. In this paper, we introduce a new geometric
constant IB(X) to measure the difference between Birkhoff and isosceles
orthogonalities in the entire normed space X. To consider the difference
between these orthogonalities, we also treat constant BI(X).