Fractional Lengths Practice: Tangent Geometry with Logarithms, Mean, and Varianc

This example demonstrates how to model “fractional lengths” (lengths divided by ratios) using a combination of geometric constructions and function/tangent visualization. It links the idea of proportionate segment length with tangent-line geometry while also using logarithmic-function behavior and statistical summaries to build intuition about averages and variability. Key concepts include fractional measurement on segments, tangent line construction (tangent geometry and tangency relationships), logarithmic functions for shaping the graphical relationship, the arithmetic mean for central tendency, and variance for spread; it is also framed to support intuition connected to stochastic/random-process thinking. Construction-wise, the example is centered on the main drawing object pic1, which serves as the canvas; the interactive work typically couples graphing/tangent features with fractional-length markers and overlays quantitative indicators associated with mean/variance. Suitable for advanced secondary students and early university learners, especially for lessons on connecting geometry with function graphs and for integrating statistical interpretation into modeling tasks.