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To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.
The Expanding Universe..
Loci: Convergence
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Euler Squares
Solving Euler Squares of Order Five
Euler squares were introduced on the first day of a problem solving class for mathematics teachers. Nineteen teachers were placed in collaborative groups and given a pegboard holding five different geometric shapes in five different colors (see Figure 4). The author acknowledges ETA Cuisenaire for providing the six Geo-Shapes Pegboards for her research.
Figure 4: a Geo-Shapes Pegboard
Challenged to find a way to place the pegs so that no shape or color repeated in any row or column, groups were observed using three methods to find a solution: diagonalization, the knight’s move, and Sudoku skills.