Pythagoras: proof + real life

A 2,500-year-old rule that is still everywhere: a² + b² = c² 📐

1. THE RULE: in a right triangle, square the 2 short sides and add them. You get the long side squared. 3² + 4² = 9 + 16 = 25 = 5².

2. THE PROOF: put 4 identical triangles in one box of side (a + b). The empty space is c². Now just slide the triangles. Same box, same triangles, so the empty space is the same: it's now a² + b². So a² + b² = c² ✓

3. REAL LIFE:
📺 A TV's size is its diagonal: 48 in × 27 in → √(48² + 27²) ≈ 55 in
🪜 Ladder: 3 m from the wall, 4 m up → you need 5 m
⚡ AC circuits: a resistor and a coil act at 90°, so impedance Z = √(R² + X²). 3 kΩ and 4 kΩ → 5 kΩ