Tricks of number patterns

TheTreeSpyder

TheTreeSpyder

Branched out member
Location
Florida>>> USA
Mr. Trachtenberg as a mental exercise; without paper or pen, while awaiting to die in a concentration camp; maintianed a sharp mind by devising new paths thru numbers. Also, jsut living to tell his students about it. It is said he was liberated 6 days before execution. i read his lil'book in 5th grade; it showed me there were both: other paths and that numbers were related. This totally changed how i looked at numbers. i have gotten many kids excited about math with these lil'magic trix; like it's an exciting journey all of the sudden..





? X 5= (Multiplication x 5)

½ that number X 10

2468 X 5 = 1234 X 10
485034 X 5 = 242517 X 10


?5 ² (2 digit numbers squared that end in 5)
The last 2 digits will always be 25,
the first 2 digits will be = ? X (?+1)

85² = ??25; ?? = 8 X (8+1) = 7225

45²= ??25; ?? = 4 X (4+1) = 2025


??² =AB² (2 digit numbers squared)

{(A X 10) X (AB + B)} + B²

87²={(80) X (87+7)} + 7² =

{(80) X (94)} + 49

7520 + 49



64²= {60 X 68} + 4²

4080 + 16



76² = {70 X 82} + 36







? X 9= (single digit multiplication by 9)

1st digit is ?-1; 2nd digit is whatever added to that makes 9

5 X 9 = 5-1 (4) for 1st digit, and 9-4(5) for 2nd digit = 45

8 X 9 = 8-1 (7) for 1st digit and 9-7(2) for 2nd digit = 72





of course being 1 number less than 10:

???????? X 9 = ???????? X 10 - ????????

(any Number X 9)

567891234 X 9 = {567891234 X 10} – 567891234



6 & 7 multiplication on attattchment, wouldn't show up in columns in post
 

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Hi Glen,

I think the HP-41CX was the best calculator HP ever build. You know back in the days when calculators were designed to last a lifetime. Though I must admit the 48 is also very nice. RPN rules /forum/images/graemlins/yup.gif.

Ken,

You probably should have put some explanations with the text. Most people can't read raw numbers/simple math identities very well. Facts and the story are two complementary part to a good presentation.

Take care,

Cary
 
Technically, RPL for the 48. I've got a 48-S rev. E ROM that I think I paid 100 bux for in the early '90s and a rev. J that I later got for 25 bux from Educalc, who handled the distribution of the remaining stock HP released after the year warranty period was up following the discontinuation of that model. It came with the soft case, but not the pocket guide.

The "original" one suffers from one of the two hinges on the ENTER key having been broken by an over-zealous nephew (who's currently a hot-shot instrumentation tech on the new USS Reagan!) playing an intensive game. So I have to press on one side of the key or it merely rocks. I suppose one day the remaining hinge will break, but between the two units I firmly believe I'll be set for life. I love the tactile feedback of the key switches, and with the caps being double-shot molded items, the legends will never wear off. The only real gripe with that model is the low-contrast display. I mainly use it in the manner of the attached image.

I carry a 32-SII when doing construction layout/framing. I set the display flags to return values based on the nearest 1/16" simplified fraction, and the package is perhaps the most usable/pocketable design ever made. Need to mark something every 12.2"? Punch the ENTER key a few times to fill up the stack with the calculated result, stretch the tape measure out, mark the first one, hit "+", mark the next, hit "+", mark the next, ad infinitum. I don't know how the Egyptians got along without one back in the day!

The 32 was my first foray into computer programming. I stepped up through a 42S to the 48 and then had to get a PC to "talk" to it :) I'm actually a relative computer newbie.

(found out about Linux due to a post on the comp.sys.hp48 newsgroup via the HPBBS which announced the [attached image] program)

Happy computing to you,
Glen
 

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Ken,

See my reply to your PM for the general equation and a couple of other things.

Glen,

I started with a used HP-76 that came without a manual. It was fun figuring out how to program it by trial and error. For construction work I use a Construction Master IV. I am assuming the fractional conversion is done after the addition or is for display only.

I had a PC board designed once where the technician, an incompetent fool, laid out the location for the package pins incorrectly because he convert from metric and then multiplied to get the pin locations. Since it was only 12 pins it looked like it was right, but it was impossible to get it to connect correctly. Once we looked at it under a microscope it was obvious what he had done. Those darn rounding errors add up.

Cary
 
Cary,

The value is for display only. There is a pair of pixels (up/down triangles) in the corner of the panel which indicate the direction from the displayed result to the actual value if they differ. The display is quite "contrasty" as compared to the 48. Here's the earlier version of the 32:

32s.jpg


Czech out http://www.hpcalc.org/ and the blurb about the new device from former HP employees.

I believe you can now fetch copies of the ROM for the HP-48 and HP-49 there (hpcalc.org), and x48 will run either in its later versions, along with the appropriate "skin". Obviously, display contrast is not a problem for x48.

Even 1/16" is quite a bit anal for just about anything construction prior to the finish carpentry.

:)
 
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