|A Most Unusual Number, on the 10c/11c/12c/15c|
Message #1 Posted by Katie Wasserman on 14 July 2010, 11:44 p.m.
I was thinking about the keyboard test timeout on the Voyagers and what it left on the display. See this thread for a little background.
If you start the keyboard test (turn off the calculator, hold down the divide key then press ON) on any of the original Voyagers (and the 12C+) and let it time out -- a few minutes, but only 2 seconds on the 12c+ -- you're left with a number ranging from 0.1 to 4.0 on the display after you clear the "Error 9" message. This number is apparently there it indicate the last key pressed that registered correctly starting with .1 (no key pressed) ending at 4.0 (sigma+ key pressed). However, these are not your run of the mill numbers, they have some very weird properties, some of which are potentially useful in programs.
1) Start the keyboard test but don't press any keys, let it time out, then press ENTER to clear the "Error 9" message
2) Store the ".1" shown in register 0, just to have it around to play with.
3) Take the reciprocal of it. It's zero, but there's more.... try 123.456 RCL 0 /, You'll see 234.56.
Dividing this magical number into any other number results in the removal of the left most digit followed by a divide by a real 0.1.
The exception is when you divide this number by itself, it returns 1.
Here's another magical property of this number:
RCL 0 Ln returns 1, it's a pseudo Euler's number.
I haven't explored it's complex properties on the 15c, but I'll bet that they are equally interesting. I also haven't explored any of the other numbers that can be gotten to using the keyboard test timeout.
On the 16C, you can see that this is one strange number. It displays as an impossibly large binary number based on the word size but it can't stored nor used in calculations, not even in floating point mode. Other models of the 12C don't timeout the keyboard test so you can't get to this number on them.
I'm curious if anyone here has explored these numbers and what else they might allow the Voyagers to do.