On the Johnson–Tzitzeica Theorems and the Yang–Baxter Equations
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: The current paper deals with the sets of Johnson circles, and to the famous Yang- Baxter equations. The Johnson–Tzitzeica theorem could be considered a result related to symmetry. we will also present an asymmetric construction related to the Johnson–Tzitzeica theorem. Then, there is a special section discussing on the Yang-Baxter equations. The concluding section attempts to connect the two above topics.