Visualizing Generators in Euler Circles

Imag­ine a large circle rep­re­sent­ing all el­e­ments of $\mathbb{Z}_n$. Inside, shade the subset cor­re­spond­ing to the gen­er­a­tors:

• For $n = 5$, the shaded subset in­cludes all $1, 2, 3, 4$.
• For $n = 6$, only $1$ and $5$ are shaded as gen­er­a­tors.

This vi­su­al­iza­tion helps to see which el­e­ments have the power to gen­er­ate the entire group through re­peat­ed ap­pli­ca­tion of the group op­er­a­tion.