Geometric Visualization of an Irish Logarithm (Log-Scale Construction)

This example demonstrates the “Irish Logarithm” idea by combining a geometry construction with a labeled numerical table, making the log-scale behavior visually understandable. It highlights how logarithms convert multiplication/division into addition/subtraction on a suitable scale. The core concepts are logarithms and their functional structure (logarithmic/ exponential equivalence), proportional relationships underlying multiplication and division, and the use of measured lengths as geometric proxies for numeric quantities. Construction-wise, it uses GeoGebra commands Element, Length, and TableText: Element selects and references key objects (e.g., t1, t2 and geometric parameters a–f), Length computes the relevant distance measures from those objects, and TableText formats the extracted values into a readable table. The included text objects (text1–text8) provide the necessary labels to connect the geometry with the log values. Suitable for secondary to early university students learning logarithmic functions, as well as for interactive graphing/geometry-based exploration.