GUNTER WEISSPedal points revisitedThe classical construction of a pedal point needs a pole O and a line l, which is intersected by a line n through O and orthogonal to l. This starting idea is adopted by many different research topics, their results are partly well-known, partly hidden in publications, which are not easy to discover. A first branching up starts with {l} being a discrete set of lines on one hand and on the other that {l} is a continuous set and O fixed. While standard treatment in both cases is based on Euclidean orthogonality, one could of course replace this by other (extrinsic or even intrinsic) orthogonality concepts. For pedal constructions in higher dimensions one can even use a “polar space” o instead of a pole O. To make sense the “space” Λ (of a continuous set) should be skew to o and define a common normal space with o, that intersects both, o and Λ in points. In a 3-space with a pole O resp. a polar line o, Λ can be a plane or a line, resp. a line only. |