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Relative Velocity and Geometry v. Analysis

originally posted to physics

I've been looking over inertial frames and relative velocity because every (recent) textbook skims over the concept with cursory diagrams and algebraic hand-waving.  On a hunch that an older textbook would provide a rigorous, geometric deduction, I picked up my roommate's University Physics of 1964 and to my utter surprise (<--sarcasm) were pages of graphs, definitions, deductions, -- a satisfying treatment that begins with Galileo and ends with Lorentz transformations.  Relativistic terms like "time dilation" and "Lorentz contraction" are more vivid than ever because I can "see" them, and I don't mean the superfluous "seeing" some rod supposedly shrinking in the margin, rather I mean the trig is all there, the deductions gradually build up page after page, etc.  This isn't the first time an older textbook approached the concept geometrically instead of analytically (by "analytically", I mean one or two diagrams followed by a plethora of algebraic deductions).  The really old texts are filled with geometric deductions: just flip through your library's copy of Principia Mathematica.

Was there merely some change in textbook style or has analytic mathematics really deprecated geometry, as I hear rumored in the math hall?  Personally, I believe Brain devised some evil plan for analysis to take over the world, but I'm just paranoid ... that or I am ageist and prefer the 60's and 70's to this 21st rubbish.

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