Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

# IllustrationLevi-Civita symbol: Cyclic (even) permutation of indices

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An even (cyclic) permutation of the indices $$\class{blue}{i}$$, $$\class{red}{j}$$, and $$\class{green}{k}$$ of the Levi-Civita symbol $$\varepsilon_{\class{blue}{i}\class{red}{j}\class{green}{k}}$$ results from rotating the indices clockwise (or counterclockwise) like this:$\varepsilon_{\class{blue}{i}\class{red}{j}\class{green}{k}} ~\rightarrow~ \varepsilon_{\class{green}{k}\class{blue}{i}\class{red}{j}} ~\rightarrow~ \varepsilon_{\class{red}{j}\class{green}{k}\class{blue}{i}}$