Pi Distribution: Integral Under Normal Curve

① This example demonstrates the appearance of π in the integral of a normal distribution curve, showing that the total area under the probability density function equals 1. ② Core mathematical concepts include normal distribution, probability density function, definite integral, π, and the interplay between geometry and probability, with references to Pythagorean theorem and spheres as auxiliary geometric elements. ③ Construction details: The GeoGebra commands Integral and Segment are used; objects include distribution parameters d, mean μ, standard deviation σ, function f, integration bounds a and g, points A, B, C, D, E, F, text labels, a sphere r, cylinder h, and sliders m and n for dynamic parameter adjustment. ④ Suitable for high school to university-level mathematics education, particularly in calculus, probability and statistics, and geometry courses, helping students understand the relationship between integration and probability distributions, and the unity of π across different mathematical branches.