Pathway XV

∂Calculus and differential geometry

Slopes from shrinking secants, area from rectangles, and curvature as how fast the tangent turns.

1. 01The tangentA secant through two nearby points becomes the derivative as they meet.5 min
2. 02Why 2xx² grows faster as x gets large. Its tangent slope is exactly 2x.4 min
3. 03Riemann sumsArea under a curve is the integral. Rectangles become the truth as n grows.5 min
4. 04CurvatureA curve bends. Curvature is how fast the tangent turns — circles have constant κ = 1/R.5 min