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 https://tinyurl.com/yvp5udm6 Great history of hyperbolic functions by Janet Heine Barnett: https://www.maa.org/sites/default/files/321922717729.pdf.bannered.pdf Very good wiki summary of hyperbolic function maths. Check out in particular the section "Comparison with circular functions" and "Relationship to the exponential function" https://en.wikipedia.org/wiki/Hyperbolic_functions Squeeze mapping and Lorentz transformation https://en.wikipedia.org/wiki/Squeeze_mapping Minute Physics video "Lorentz Transformations | Special Relativity Ch. 3" https://www.youtube.com/watch?v=Rh0pYtQG5wI Stackexchange discussion of the different ways to pronounce the hyperbolic functions: https://math.stackexchange.com/questions/176055/pronunciation-of-sinh-x-cosh-x-tanh-x-for-short Bug alert: The 1 s here https://www.youtube.com/watch?v=G0Fa5Zl-Z3c 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.) -An arc angle may pay you a visit if you sin too much :) 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