Simple visual logarithms and hyperbolic trig

2023-08-05

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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

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"

/youtube/video/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 /youtube/video/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