Step 1: A (10,10) armchair carbon nanotube has diameter d ≈ 1.36 nm. Is it metallic or semiconducting? Step 2: Rule: metallic if n − m is a multiple of 3. Step 3: n − m = 10 − 10 = 0 = 3×0 → metallic. Step 4: All armchair (n,n) tubes are metallic — they conduct like copper wires only 1 nm wide, carrying ~10⁹ A/cm² (1000× copper's limit). Step 5: Contrast a (10,0) zigzag tube: n − m = 10, not divisible by 3 → semiconducting, usable as a transistor channel. Result: Chirality (n,m) decides electronic character — the same carbon atoms, rolled differently, give a metal or a semiconductor.