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OT: Mathematical Curiosity (NOT Primes ;-)

OT: Mathematical Curiosity (NOT Primes ;-)...

x + LOGe(COSH(x)) = -693.147m for LARGE negative x

Playing around with that expression I was expecting it to approach zero.

Any significance to that number -693.147m ?

Like Avocado's number or something like that ?>:-}

(BTW, That expression makes perfectly smooth PWL break-points, with nice smooth derivatives... simulator-friendly ;-) ...Jim Thompson

-- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | San Tan Valley, AZ 85142 Skype: skypeanalog | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at

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| 1962 | I love to cook with wine. Sometimes I even put it in the food.

Reply to
Jim Thompson
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As in...

...Jim Thompson

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| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
           The touchstone of liberalism is intolerance
Reply to
Jim Thompson

Wolfram Alpha says the limit as x goes to negative infinity is -log(2) so it looks like you have a decimal point position problem...

formatting link
+-infty+x+%2B+log%28c osh%28x%29%29&x=0&y=0

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Reply to
bitrex

[snip]

Nope, no decimal point problem LOGe(2) = 693.1472m

I hadn't recognized that. Thanks! ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
           The touchstone of liberalism is intolerance
Reply to
Jim Thompson

log(2) is also the infinite sum of the alterating harmonic series: 1 - 1/2 + 1/3 - 1/4 + 1/5 etc.

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Reply to
bitrex

Ah I missed the "m"...

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Reply to
bitrex

I think it should be straightforward to prove using ya friend L'Hospital's rule.

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Reply to
bitrex

[snip SIG which inadequate reader left as detritus :-]

I got there in a bass-ackwards fashion... by exploring the integral of TANH, which I knew I wanted as the derivative of whatever I came up with. ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
           The touchstone of liberalism is intolerance
Reply to
Jim Thompson

What is "m"? Is that your way of saying 0.6931472?

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Rick
Reply to
rickman

cosh(x)=[exp(x) + exp(-x)]/2, doesn't take very large negative x for this to be real close to exp(-x)/2. You figure the rest out...Avocado's number? ?? His full name is Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di C erreto. I'll give you the rest of your life to memorize it.

Reply to
bloggs.fredbloggs.fred

How long did it take Avogadro?

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Rick
Reply to
rickman

ln(2)

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John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com
Reply to
John Larkin

this to be real close to exp(-x)/2. You figure the rest out...Avocado's num ber??? His full name is Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto. I'll give you the rest of your life to memorize it.

About 5 seconds, he was REALLY smart.

Reply to
bloggs.fredbloggs.fred

Sure! I'd like to see more of that! I/O libraries, Excel, calculators, etc., should all be able to understand and print that format. What's easier to read: 0.000000001 or 1n?

I made a little Unix command line calculator similar to 'dc' which does this. Only 31kB compiled. I'm old fashioned, I like it compact.

Jeroen Belleman

Reply to
Jeroen Belleman

Avogadro never got to know how big his number was.

Jeroen Belleman

Reply to
Jeroen Belleman

My son, Aaron, wrote a utility for me that can parse netlists and reduce equations with m, u, n, p, f, etc., to a final number. Handy for generating subcircuit models. ...Jim Thompson

--
| James E.Thompson                                 |    mens     | 
| Analog Innovations                               |     et      | 
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    | 
| San Tan Valley, AZ 85142   Skype: Contacts Only  |             | 
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  | 
| E-mail Icon at http://www.analog-innovations.com |    1962     | 
              
           The touchstone of liberalism is intolerance
Reply to
Jim Thompson

What's wrong with the 1e-9 that they all currently use?

Excalibur, for those who like RPN... or Forth

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Rick
Reply to
rickman

The question was about learning his full name. It hit me that it must take a while for a kid to learn his full name when it is that long. I bet his mom didn't use it all when calling him for dinner. It would get cold.

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Rick
Reply to
rickman

ln(2) is positive. So it is -ln(2) or ln(93.343e-303).

Reply to
John S

His given name was Lorenzo so she probably called him enzo or renzo.

Reply to
bloggs.fredbloggs.fred

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