On the Generalization of Iso-Taxicab Geometry

In this study, we defined a new geometry which generalized the taxicab geometry and Iso-taxicab geometry. In the coordinate system of this geometry the angle between X -axis and Y -axis is α( 60°≤ α ≤90° ). In addition, we defined distance function on the six hextants divided by three axis. We used the method to define the distance function in Iso-taxicab geometry. Unlike the form of circles are regular hexagon in the Iso-taxicab geometry, that in the Iso-taxicab geometry is a hexagon whose three pairs of opposite side are parallel. Also we defined the angle ``g-radian`` which can apply to the new coordinate, and calculated the different form of trigonometric functions on every hextants. The methods and results in this study can be used at the research of plane geometry in the generalized Iso-taxicab geometry.