HP Forum Archive 14

[ Return to Index | Top of Index ]

Math not button-pushing Message #1 Posted by bill platt on 1 July 2004, 4:17 p.m. Hi Ed, My son (7 in August) knows that I enjoy calculators. He said the other day, "so Daddy, you love calculators very very much." To which I replied, "Oh, I don't know that I *love* them, but I *do* enjoy using them and thinking about their design." So, being a collector, one must be careful. Actually, I have "indoctrinated" my son regarding the correct, effective use of these machines, and the *need*, yes NEED, to do as much arithmetic as possible in your head. (We need to do it, becase you cannot be efficient with numbers unless you use them frequently---and it is a skill of tremendous value----my mentor used to out-compute me in his head---and I had an 11c and though I was so smart. But he used a calcuator instead of trig tables when required.) The other day, I taught my sone some of the "rule of nines" which he did find fascinating (no calculator involved). The next day, he told me that he really loved that--and that he wanted to do more math with me. So we applied the "rule of nines" to 8's and 7's...and in the process I introduced both summation by columns, and multiplication, and the commutative property, for both addition, and also multiplication, and why this is..... All lot's of "fun" and no calculators! ((In fact, I don't see how the calculator would be useful---it just "spits out" answers. The fun of numbers and math is understanding how stuff happens---which is why we like calculators: we like programming them (which requires you to understand what the solutions) and we like deconstructing calculators---like the thread on matrices recently with all the heavy-hitters (V.A., P.O.H, K.S., Eam., L.C.V., J-F.G., VPN, B.W., A.M.....)--all trying to figure out the subtleties of machine results at far decimal places.....)) But both my children like the 48GX---they think it is novel and fun to be able to write letters on the screen, and make it "beep". Regards, Bill

I do agree with you! (N.T.) Message #2 Posted by Marx Pio on 1 July 2004, 10:10 p.m., in response to message #1 by bill platt -

Re: Math not button-pushing Message #3 Posted by Eddie Shore on 1 July 2004, 10:55 p.m., in response to message #1 by bill platt I believe it is why we use more powerful calcualtors to explore mathematics and to understand reason. More often than not, I find myself first estimating quick calcualtions in my head then using the calculator to verify. I estimate that those who don't like math see calcualtors as "push and get answer". But that will never allow people to see the ultimate power of such a machine.

Re: Math not button-pushing Message #4 Posted by OpenRPN on 2 July 2004, 1:18 a.m., in response to message #1 by bill platt I couldn't agree more. A calculator is a tool: not a brain replacement. During the first day of my freshman engineering analysis (read: math for sadists) course, the professors made it very clear that no calculators were needed or could even be used during exams. Their logic being that engineers *design* calculators and must understand from whence the answer originates.

Re: Math not button-pushing Message #5 Posted by KC on 2 July 2004, 5:18 a.m., in response to message #4 by OpenRPN I believe that "one who loves calculator loves Maths", and the opposite is also true: "one who doesn't love Maths doesn't love calculators (but the reverse isn't necessary true: one who loves Maths doesn't necessary love calculators)". So, all people in this forum, I believe, have good senses on Maths and numbers.

Re: Math not button-pushing Message #6 Posted by Bram on 2 July 2004, 6:26 a.m., in response to message #1 by bill platt Quote: In fact, I don't see how the calculator would be useful---it just "spits out" answers. The fun of numbers and math is understanding how stuff happens Sometimes things go on vice versa when the calculator "spits out questions", as happened to me the other day. I was rather thoughtlessly pressing some keys and at the end of a vague mental path (that cannot be reconstructed) my calculator raised some numbers and only then I started to think. But first, dear friends, take all your favorite calculator and compute the reciprocal of 7.4 Now that turns out a nice number, doesn't it? At first I considered this just a pretty coincidence, worth to remember. But then I started to search for more numbers like these. Perhaps there were patterns to be found. Perhaps I could write a program to find "nice combinations". While still thinking on that, I've found two more numbers of different "nicety": 5.5 and 7.992 It's not of earthshaking importance, but it was fun to me. In this case my calculator definitively didn't make my life easier, but without it I wouldn't have discovered this interesting bit. And I'm sure it will help me to find some answers. A real reciprocity between man and machine.

Re: Math not button-pushing Message #7 Posted by Valentin Albillo on 2 July 2004, 6:40 a.m., in response to message #6 by Bram Bram posted: "take all your favorite calculator and compute the reciprocal of 7.4 [...] A real reciprocity between man and machine." "Pun intended", I suppose ? :-) Best regards from V.

You noticed! Message #8 Posted by Bram on 2 July 2004, 7:40 a.m., in response to message #7 by Valentin Albillo Thanks for your pat on my (Dutch) back.

Re: Math not button-pushing Message #9 Posted by Garth Wilson on 2 July 2004, 2:14 p.m., in response to message #6 by Bram I'm sure most others have noticed this, but 1/7, 2/7, 3/7, 4/7, 5/7, and 6/7 are interesting as repeating decimals because they're all the same-- the cycle of repetition just starts in different places.

Re: Math not button-pushing v.v. Message #10 Posted by Bram on 4 July 2004, 1:51 p.m., in response to message #6 by Bram I've restricted the "nicety" of the numbers to those that match the pattern 0.abcabcabc...(ad infinitum) and with a program for HP-32SII I found 36 of these numbers whose reciprocal value is a decimal value of only a few digits followed by zeros. (maximum of 3 decimal digits. With max. 4 you get 7 (is odd) numbers extra) F.e. 0.216216etc. has a reciprocal value of 4.6250000... The whole set includes trivial numbers like 0.111111... and 0.333333... as well (although 0.777777... is the only one lacking) Now let me define the notation N(abc) being 0.abcabcabc.... I've noticed that sometimes two numbers form a pair by this relation: 1/a.bc => N(klm) and then 1/k.lm => N(abc) examples: 1/1.08 => N(925) and 1/9.25 => N(108) 1/2.25 => N(444) and 1/4.44 => N(225) but they do so only with 2 decimal digits (2nd may be 0) 1/5.40 => N(185) and 1/1.85 => N(540) otherwise digits will overlap. with 3 "decdigs" 1/4.625 => N(216) but 1/2.16 => 0.4629629629 (=0.4625+0.0004625 etc.) Just some funny observations. I'm not considering a thesis of any kind ;-) I just played with the calculator, wrote a program, watched the results and thought them over. No maths involved, only number crunching. Like I said before: somtimes it's the other way round.

Divisors - I liked it :) Message #11 Posted by Tizedes Csaba [Hungary] on 7 July 2004, 7:56 p.m., in response to message #10 by Bram When I was young I made similar "observations", It was wonderful: 1/22=0.0454545... and 1/45=0.0222222... 1/18=0.0555555... and 1/55=0.0181818... 1/33=0.0303030... and 1/30=0.0333333... 1/99=0.0101010... and 1/10=0.1 == 0.0999999... and so on... All of this numbers are divisors of 990. Csaba

Re: Math not button-pushing Message #12 Posted by John Smitherman on 2 July 2004, 3:19 p.m., in response to message #1 by bill platt Bill, your children may be too young to enjoy or benefit from this handbook now but I believe that it's a great resource for anyone who is working, studying or has interest in the fields of math, science or engineering. Schaum's Mathematical Handbook of Formulas and Tables by Murray R Spiegel It's available from Amazon for ~$12 http://www.amazon.com/gp/reader/0070382034/ref=sib_dp_pt/002-4216030-3468813#reader-link I like being able to look at page after page of tables of numbers, formulae, plots and geometric shapes in such a concise collection. If anyone has another favorite please pass it on. Regards, John

Re: Math not button-pushing Message #13 Posted by Dave Shaffer on 3 July 2004, 2:07 p.m., in response to message #12 by John Smitherman "If anyone has another favorite please pass it on." The CRC Math table book! When I occasionally talk to high school students about science, I bring along my tattered copy (from about 1965!) to emphasize how useful it would be for them to get one when they go to college. (The trig, log, etc. tables are no longer needed, of course, if you have a calculator handy, but the trig conversions, integrals and differentials, probability tables, etc. are still most useful.)

Re: Math not button-pushing Message #14 Posted by Bill (Smithville, NJ) on 6 July 2004, 3:45 p.m., in response to message #13 by Dave Shaffer Dave, >> The CRC Math table book! You hit the nail - That book got me trough college and many of my early engineering jobs. I still have a copy - (just checked - 21st eddition, 1973) and still refer to it. A great reference. Of course, when I was in college in 1967, a slide rule and the CRC was all a student needed. Bill

Re: Math not button-pushing Message #15 Posted by Tom Scott on 4 July 2004, 2:48 p.m., in response to message #12 by John Smitherman "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" Edited by M. Abramowitz & I.A. Stegum (National Bureau of Standards, Dept. of Commerce).

Re: Math not button-pushing Message #16 Posted by John Smitherman on 6 July 2004, 9:54 a.m., in response to message #15 by Tom Scott Thank you for the feedback Dave and Tom. John

[ Return to Index | Top of Index ]

Go back to the main exhibit hall