Curtis Duane Tuckey

Higher Trigonometry, Hyperreal Numbers, and Euler's Analysis of Infinities

Often I have considered the fact that most of the difficulties which block the progress of students trying to learn analysis stem from this: that although they understand little of ordinary algebra, still they attempt this more subtle art. From this it follows not only that they remain on the fringes, but in addition they entertain strange ideas about the concept of the infinite, which they must try to use. Although analysis does not require an exhaustive knowledge of algebra,

Finding small rotations and translations in imperfect part and die models

Abstract Automatic verification of part and die models can be hampered by the presence of rigid-motion deviations of a model from its baseline coordinates, in addition to imperfections in the model. A coordinate measuring machine (CMM) searches for a physical point in a specified neighborhood. If it finds a point at the location where nominal data indicates a point, the model is verified at that point; otherwise, a measured deviation is given. One problem is that the physical point on the model whose coordinates are measured may not be the same as the prescribed point whose coordinates are given in nominal data. This report includes a procedure for detecting rigid-motion deviations from nominal in a model-verification environment.