similarity basedonnotesbyolegviro revisedbyolgaplamenevskaya euclidean geometry can be described as a study of the properties of geometric gures but not all kinds of conceivable properties only the properties which do not ...
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...Similarity basedonnotesbyolegviro revisedbyolgaplamenevskaya euclidean geometry can be described as a study of the properties geometric gures but not all kinds conceivable only which do change under isometries deserve to called and studied in euclidian somegeometric are invariant transformations that belongto wider classes one such class is roughly they preserving shapes changing scales magnifying or contracting part studies unchanged by introduced number dierent ways most straightforward them based on notion ratio segments thesimilarity an integral fact there no interesting phenomenon belong does survive rescaling this sense whole considered through glass moreover results concerning relations among distances obtained using however main notions emerge traditional presenta tions particular kiselev textbook very indirect way below it shown how done more naturally according stan dards modern mathematics rst sections denitions for distance summarized commensurable see detailed treatment ma...