Abstract
This paper researched three definitions of Gauss map and found that the definition of “Gauss map” in the paper of Arasomwan and Adewumi may be incoherent with other publications. In addition, we analyzed the difference of continuous Gauss map and the floating-point Gauss map, and we pointed out that the floating-point simulation behaved significantly differently from the continuous Gauss map.
Highlights
It is suggested that the authors either remove the phrase of “Mouse map” or replace formula (9) with formula (2)
Suppose Arasomwan and Adewumi [1] used Definition 2; another paradox was raised between the continuous model (see formula (1)) and the floating-point simulation
For the floating-point simulation, we found the two properties of continuous model were changed by the following facts
Summary
The authors give an inappropriate definition of Gauss map (Gaussian map) that some readers may get the mistaken understanding. The first definition is used in differential geometry, where the “Gauss map” maps a surface in Euclidean space R3 to the unit spheres S2; that is, given a surface X lying in R3, the Gauss map is a continuous map N : X → S2 such that N(p) is a unit vector orthogonal to X at p, namely, the normal vector to X at p. The second definition of Gauss map is related to continued fractions and is used in programming, chaos, ergodic theory, and so forth.
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