Give ten people the same wealth and the line runs straight — perfect equality. Take from the many and give to the few and the line sags into a bow; the area of that bow, doubled, is the Gini coefficient. Drag any bar to move wealth around, and watch the curve bend and the number climb.
The Gini coefficient is computed exactly from the wealth you set: sort the values, build the Lorenz curve (cumulative share of wealth against cumulative share of people), and Gini = 1 − 2·(area under the curve) = twice the area between the curve and the equality diagonal. Drag any bar and both update live — perfect equality gives Gini 0 (the straight line), one person holding everything approaches 1. Standard, real inequality mathematics.
Ten people stand in for a whole society and wealth is a single number; real distributions have millions of people and debt (negative wealth), and the Gini is one summary that hides the shape — two very different societies can share a Gini. The measure itself, the area between the Lorenz curve and equality, is exact.