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Elementary Mathematics from a Higher Standpoint
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_This three-part treatment on mathematical knowledge needed by teachers was a pathbreaking book published by the German mathematician Felix Klein between 1924 and 1928 and it is still as relevant as it was 90 years ago. The books pulse with the excitement of the actual lectures they came from and combine geometric intuition with the precision of arithmetic formulas in an inspiring way.§§The second volume begins with an analysis of the simplest geometric manifolds such as line segments, and area and volume as relative magnitudes. The second section on geometric transformations examines affine and projective transformations, higher point transformations, transformations with change of space, and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations.§
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