To describe the geometry of normed space, many geometric constants have been investigated. Among them, the von Neumann–Jordan constant has been treated by a lot of mathematicians. Here we also consider Birkhoff orthogonality and isosceles orthogonality. The usual orthogonality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality is not symmetric in general normed spaces. A two-dimensional normed space in which Birkhoff orthogonality is symmetric is called Radon plane. We consider the upper bound of a geometric constant in Radon planes. Then we estimate the von Neumann–Jordan constant in Radon planes.

为了描述赋范空间的几何形状，已经研究了许多几何常数。其中，冯·诺伊曼–乔丹常数已被许多数学家对待。在这里，我们还考虑了Birkhoff正交性和等腰正交性。内积空间中的通常正交性和赋范空间中的等腰正交性是对称的。但是，伯克霍夫正交性在一般赋范空间中不是对称的。Birkhoff正交性对称的二维范数空间称为Radon平面。我们考虑了Radon平面中几何常数的上限。然后，我们估计Radon平面中的von Neumann–Jordan常数。