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Ollerenshaw, Kathleen. Some personal delights in geometry---from earliest days to fractals. Bull. Inst. Math. Appl. 27 (1991), no. 4, 65--75. SC: 01A99 (51-03 58-03), MR: 1 110 875.
Dame Kathleen Ollerenshaw discusses some of her favorite results and ideas of geometry. The examples range from Euclid to the present, and include illustrations of projective geometry, a fixed point principal (two superimposed identical maps on different scales will share a point in common), the nine-point circle (with proof), Pascal's mystic hexagram theorem and its generalization to general conics, and Briachon's theorem, obtained as the dual of Pascal's theorem. She briefly discusses the attempt to represent astronomy in geometrical terms, mentioning a frantic search for a "Clock in the Sky" for navigational purposes, achieved to some extent by observations of the moons of the planet Jupiter. She closes with some illustrations and a brief discussion of fractals. One of her examples is her own (apparently new) observation that if one has three circles intersecting in pairs, the three chords joining the points of intersection meet in a point; a proof is given in the article The Ollerenshaw point. Closely related topics: Geometry, Projective Geometry, Geometric Fixed Point Principles, Astronomy, The Reckoning of Time, and Fractals.