Note
Turning a circle inside out
Inversion in a circle swaps its inside and its outside: points near the center are sent far away, and far points come close. It turns circles through the center into straight lines, and it keeps the angles between curves.
Firsthand Math shows mathematics in figures you can move. Digestions take a recent result apart; notes are one idea and a figure to try it with.
Turán's theorem, from edges to eigenvalues
Turán's theorem bounds the edges of a graph that has no clique of a given size. Its spectral version bounds the largest eigenvalue of the adjacency matrix instead, and gives the original back in two lines.