Stage 7 of GEOMGBITS: seven trials in scaling and similarity — the most powerful idea in the track. Scale a shape by k and its lengths go ×k, its areas ×k² and its volumes ×k³. And because every constant cancels in a ratio, comparing two circles never needs π at all.
Each trial is locked until you clear the one before it. Every level scores out of 1000 — 600 for accuracy, 400 for speed — so speed alone can't clear the bar; you have to solve most problems, and quickly. Reach 650 to unlock the next.
You can carry one scale factor across a whole figure, jump from lengths to areas and volumes by squaring and cubing, work backwards from an area ratio with a square root, and compare two circles without π ever entering the arithmetic.