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Simple visual logarithms. Is there such a thing? You bet :) 00:00 Intro 01:59 Rubik's cube and drill 03:26 What's the area? 05:15 Sum of 1 1/2 1/3 ... 06:35 Mystery sum 11:32 What base? 17:25 What is Log_b(x)? 22:14 Is this a circle? 28:53 Proof that e^a = cosh(a) sinh(a) 30:50 Thanks Maths of spinning cubes by Lingguo Bu Great history of hyperbolic functions by Janet Heine Barnett: Very good wiki summary of hyperbolic function maths. Check out in particular the section “Comparison with circular functions“ and “Relationship to the exponential function“ Squeeze mapping and Lorentz transformation Minute Physics video “Lorentz Transformations | Special Relativity Ch. 3“ Stackexchange discussion of the different ways to pronounce the hyperbolic functions: Bug alert: The 1 s here should be x s :( Some neat comments: Call the hyperbolic sine and cosine “shine and coshine“ Hmm... the multiplication by halving and doubling looks awfully like Russian multiplication - never thought of a cross link to logarithms before (In the end quite different. Still neat observation.) Music: Morning Mandolin by Chris Haugen T-shirt. Google “Yes, I'm always right!“ math t-shirt for many different versions of this t-shirt. Enjoy! Burkard
