By G. Hardy
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Extra info for A Course Of Pure Mathematics
The shaded triangle conforms to the hypothesis B 2 C 2 by design. From the intentional design, 0 one is to show or deduce that 90 in order where A 2 to prove the converse. ’ However, the year is 2008, not 1958, and the word design seems to be a superior conveyor of the intended meaning. 12: Euclid’s Converse Diagram Euclid’s first step was to construct a line segment of length B ' where B ' B . Then, this line segment was joined as shown to the shaded triangle in such a fashion that the corner angle that mirrors was indeed a right angle of 90 measure—again by design!
50 Note: as is the occasional custom in this volume, the reader is asked to supply all dimensional details knowing that the diagram is dimensionally correct. I am convinced that Kurrah himself would have demanded the same. P ! P P ! P P is a fixed pivot point P ! 18 clearly illustrates, Kurrah took a cleverly dissected Bride’s Chair and masterfully packed it into the big square though a sequence of rotations akin to those employed by the toy Transformers™ of today—a demonstration of pure genius!
The downside is that visual intuition plays a minimal role as similarity arguments produce the result via a few algebraic pen strokes. Thus, this is not a suitable beginner’s proof. ) and algebraic terseness. Thus, it is included as a major milestone in our survey of Pythagorean proofs. To summarize, Legendre’s proof can be characterized as an embedded similarity proof where two smaller triangles are created by the dropping of just one perpendicular from the vertex of the master triangle. All three triangles—master and the two created— are mutually similar.
A Course Of Pure Mathematics by G. Hardy