Sizes in On Sizes: Interactive Geometric Comparison

① This interactive example demonstrates the size relationships discussed in the book 'On Sizes', visually comparing different geometric objects such as circles, triangles, and segments through dynamic diagrams. ② Core mathematical concepts include circles and incircles, similar triangles, trigonometry, inequalities, fraction representations, and upper/lower Riemann sums, integrating geometry with algebra. ③ Construction highlights: Using GeoGebra commands like Line, Circle, FractionText, Intersect, and Segment, the model builds multiple points (B, s, S, β, G', G, A, D', p, D, n, m, M, c, d, e, f, g, C, h) and text objects (text1, textP17, etc.), creating adjustable size-comparison models via intersections and segments. ④ Suitable for high school to early college students for intuitive geometric understanding, inequality proofs, and optimization explorations, also useful as supplementary material for history of mathematics or classic texts.