Ternary diagram geology
Mathematical Geosciences Springer Journals However, equal central angles do not necessarily sweep out This can be demonstrated by the fact that, in Euclidean geometry, equal central angles sweep out equal lengths of the unit circle. As noted by Thompson and Dray (2000), taxicab geometry is distinquished from Euclidean geometry by the fact that angles are not rotation invariant. The essential problem with my presentation is that these identities are incorrect for the Euclidean radians and, unlike degrees and Euclidean radians, there is no simple relationship between degrees and taxicab radians.
They should, instead, have been given in taxicab radians, as in the following: 1 − if 0 ≤ θ < 4 cos (θ ) = taxi T T −3 + if 4 ≤ θ < 8 The taxicab radians are defined in terms of the arc length of the diamond-shaped taxicab unit circle, which is shown in Figure 2 of the paper. 5, July 2004 ( 2004) Erratum Revisiting the Geometry of a Ternary Diagram With the Half-Taxi Metric In Figure 2 and within the appendix of my paper concerning the half-taxi met- ric (Miller, 2002), I expressed the identities for the taxicab cosine function in degrees. Erratum: Revisiting the Geometry of a Ternary Diagram with the Half-Taxi Metric Erratum: Revisiting the Geometry of a Ternary Diagram with the Half-Taxi Metric