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://youtu.be/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://youtu.be/G0Fa5Zl-Z3c?t=1270 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