Differential Geometry
Essential formulas and concepts in differential geometry
Curvature of a Plane Curve
\(\displaystyle \kappa(x) = \frac{|y''(x)|}{\big(1 + [y'(x)]^2\big)^{3/2}}\)
Variables:
Description/Usage:
Mathematical concept visualization
Arc Length of a Curve
\(L = \displaystyle \int_{x=a}^{b} \sqrt{1 + [y'(x)]^2}\,dx\)
Variables:
- \(y'(x) is the derivative (slope) of the curve y(x); the integral is evaluated from x=a to x=b, the x-coordinates of the endpoints of the curve segment.\)
Description/Usage:
Mathematical concept visualization