HP Forum Archive 19

[ Return to Index | Top of Index ]

Why hyperbolic functions are critical ! Message #1 Posted by gene wright on 4 June 2010, 12:26 p.m. TI had them. HP's did not. In this case, TI was correct. Hyperbolic functions were critical to avoiding doom! I saw this while watching the classic 1951 movie "The day the earth stood still" recently, which if you haven't seen, you should. Professor Barnhardt's blackboard has equations written all over it that are critical for humanity to solve to get into space. Klaatu gives him a helping hand. The equations definitely show hyperbolic trig functions. I had never noticed them until this time. Below is a picture of the blackboard, but it is too blurry to show the equations well...but they are there! Anyone find a better picture or have the DVD to capture a frame to show? :-) Who knew?

Re: Why hyperbolic functions are critical ! Message #2 Posted by Namir on 4 June 2010, 12:56 p.m., in response to message #1 by gene wright And if we can calculate hyperbolic functions (and inverses) using an HP12C, then all is good in the land! :-> Namir

Re: Why hyperbolic functions are critical ! Message #3 Posted by Ken Shaw on 4 June 2010, 1:11 p.m., in response to message #1 by gene wright I vaguely recollect that the top left part of the blackboard has some equations that you would expect to find in an introductory calculus course, not on a scientist's blackboard! (OTOH, they are at least valid equations, IIRC.) But I have the DVD. I'll see if I can grab a useful frame for you.

Re: Why hyperbolic functions are critical ! Message #4 Posted by Gene Wright on 7 June 2010, 11:18 a.m., in response to message #3 by Ken Shaw Here are the screen shots from the DVD courtesy of Ken. Thank you! As I said, hyperbolic functions were critical to avoiding destruction of the human race in 1951. TI may have simply been trying to make sure we continued to survive! Why wasn't HP interested? lol. :-)

Re: Why hyperbolic functions are critical ! Message #5 Posted by Don Shepherd on 7 June 2010, 11:29 a.m., in response to message #4 by Gene Wright Gene, I think the key to the survival of the earth is found in the first picture of your post. Bottom right corner: 0! and 0!! and 0!!!!? If we can find a way of logically explaining to students why 0! = 1, then we will have the capacity to figure out how to survive as a species. And if can explain double-factorial and quadruple-factorial, we will indeed be the supreme species!

Re: Why hyperbolic functions are critical ! Message #6 Posted by Gene Wright on 7 June 2010, 12:05 p.m., in response to message #5 by Don Shepherd Lol I'm not sure that's intended to be 0 factorial, etc, but surprise that the term turns out to BE zero. Love this movie.

Re: Why hyperbolic functions are critical ! Message #7 Posted by Norman Dziedzic on 7 June 2010, 1:53 p.m., in response to message #5 by Don Shepherd You missed the " before each term so we actually need to figure out the double derivative of the quad-factorial of 0. <hmmm>

Re: Why hyperbolic functions are critical ! Message #8 Posted by Walter B on 7 June 2010, 2:48 p.m., in response to message #7 by Norman Dziedzic Look like equal signs to me, pointing to northwest or southeast :->

Re: Why hyperbolic functions are critical ! Message #9 Posted by Gene Wright on 7 June 2010, 2:52 p.m., in response to message #8 by Walter B lol. I think it is an equals sign for the terms above it. The !!! are the surprise of Dr. Barnhardt that the terms were equal to 0.

Re: Why hyperbolic functions are critical ! Message #10 Posted by Gerson W. Barbosa on 7 June 2010, 5:41 p.m., in response to message #9 by Gene Wright Yes, one of the terms appears to be 5 / 1 7 1 \ F * | - ---- + ------ + ----- | , \ 6*3! 3*5! 5! / which is indeed equal to 0.

Re: Why hyperbolic functions are critical ! Message #11 Posted by Martin Pinckney on 7 June 2010, 9:25 p.m., in response to message #10 by Gerson W. Barbosa What is "F" in the relations?

Re: Why hyperbolic functions are critical ! Message #12 Posted by Gerson W. Barbosa on 8 June 2010, 7:29 p.m., in response to message #11 by Martin Pinckney I don't have the foggiest notion ... By the way, does anyone know if those equations have a meaning at all?

Re: Why hyperbolic functions are critical ! Message #13 Posted by Ken Shaw on 9 June 2010, 12:46 p.m., in response to message #12 by Gerson W. Barbosa In an interview, Robert Wise (the film director) said they hired an academic to write a problem in orbital mechanics on the board (or words to that effect). There's something like it here (link).

Re: Why hyperbolic functions are critical ! Message #14 Posted by Martin Pinckney on 9 June 2010, 1:39 p.m., in response to message #11 by Martin Pinckney Turns out "F" is the "hyperbolic eccentric anomaly". This is clearly explained in Spacecraft Systems Engineering By Peter W. Fortescue, John Stark, and Graham Swinerd.

Re: Why hyperbolic functions are critical ! Message #15 Posted by Eric Smith on 8 June 2010, 3:19 a.m., in response to message #5 by Don Shepherd Quote: If we can find a way of logically explaining to students why 0! = 1 Trivially. (n+1)! = n! * (n+1), by the definition of factorial n! = (n+1)! / (n+1) 2! = 3! / 3, and since 3! = 6, 2! = 2 1! = 2! / 2, and since 2! = 2, 1! = 1 0! = 1! / 1, and since 1! = 1, 0! = 1 One more step shows why (-1)! is undefined, and by extension, the factorial of any negative integers. Quote: then we will have the capacity to figure out how to survive as a species. If only it were that easy!

[ Return to Index | Top of Index ]

Go back to the main exhibit hall