How to Measure Path Length ?

Path length measuring is a relevant engineering problem. Leonardo Da Vinci designed for the military appropriate equipment, the podometer, to do so. Modern equipment such as step meters and map meters are quite similar to Da Vinci‟s design, despite geometrical statistical stereological methods based on theorems of Cauchy and Buffon that were potentially available for a long period of time for doing a better job. The theorems have moreover been applied earlier for the engineering purposes indicated in this paper. Even Saltikov‟s reintroduction for quantitative image analysis purposes in 1945 was ignored. Gradually, the last half of a century, stereological methods became more popular in concrete technology. Nevertheless, the stereology-based global averaging operation required to make the step from materials technology to engineering properties is inherent to making errors, as the literature demonstrates. The methodological framework has been described in earlier papers by this author as to path length measurements in sections of cracked concrete and on X-ray images of steel fibre reinforced concrete (SFRC). By laying side by side in this paper the direct engineering approach (from Da Vinci to map meter) and the science (stereology)-based approaches, the profit in economy and reliability can nevertheless be stressed. Particularly the element of geometric averaging based on simple mathematical-statistical notions is highlighted, because the literature reflects still major violations to these scientific principles. Three-dimensional information in the indicated fields of materials engineering is also readily obtained, provided proper sampling is guaranteed.