Wikipedia:Reference desk/Archives/Mathematics/2008 September 12

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September 12

how to predict the next number with 4 digits

what is the percentages to predict a totally exact number each time?

-if someone of you know anything details aboutthe prediction or formula applied to find a exact number with 4 digits each time,please let me know .thanks for sharing.

If I understand your question correctly, you are asking what the probability of guessing one correct number in 10000 numbers (0000 to 9999). Assorted conditions apply - the main one being that the next number is independent of the previous number. If that is the case then the answer is 1/10000 as a probability and 100 * 1/10000 as a percentage. -- SGBailey (talk) 11:26, 12 September 2008 (UTC)

What did they use before graphing calculators?

Pre-calc seems to depend on graphing calculators. But obviously they weren't always around. What did they use before the graphic calculator for pre-calc? I'm assuming the abacus and slide rule weren't sufficient. ScienceApe (talk) 21:43, 12 September 2008 (UTC)

What part of precalc requires a graphing calculator? I'm not quite sure what precalc consists of (I was educated in England), but I think you can do it all with pencil and paper. Nothing at school relies on complex calculations. Of course, there were people in pre-calculator days who had to perform complex calculations, beyond the abacus and slide rule. They used pen, paper and a lot of time and effort. Algebraist 21:48, 12 September 2008 (UTC)

I don't know. The professor just said that there are parts of the class that required a calculator, and that such problems were impossible to do without the use of a calculator (even for him). It just made me wonder how they were able to do such calculations before the graphing calc was in common usage for highschool/college students. ScienceApe (talk) 03:32, 13 September 2008 (UTC)

See Human computer for one alternative. A friend of mine asked a class when they thought the industrial revolution was, wide variations, one answer was 1960 :) Dmcq (talk) 21:51, 12 September 2008 (UTC)

True, but I don't think professional human computers were ever made available to students in high schools. Algebraist 21:57, 12 September 2008 (UTC)

Oh okay then, books of tables. Students used thin booklets of four or five figure tables, professionals used books with 7 figure tables and you learn rules to interpolate for the last couple of digits. You could get huge great big thick books with all sorts of tables including even tables of random numbers. Dmcq (talk) 22:08, 12 September 2008 (UTC)

Here's a classic professional mathematicians book of tables Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables Dmcq (talk) 22:16, 12 September 2008 (UTC)

I have to say that in my time doing maths (junior school to degree level), I only ever used a graphics calculator once or twice, and that was when we were being taught how to use them. They're banned in most exams, and I can't think of any good reason to use one really. Most graphs you don't need to actually know the exact curve, just a sketch and a few quick calculations are enough. -mattbuck (Talk) 23:10, 12 September 2008 (UTC)

That's weird. I've taken pre-calc three times so far (nothing to do with my intelligence, just school politics), and all of them require a graphing calculator. I'm not talking about Math in general, it seems only pre-calc uses it really. ScienceApe (talk) 03:37, 13 September 2008 (UTC)

Could you give us an example of a question from your textbook, or maybe from an exam, that is allegedly impossible to answer without the assistance of a graphing calculator? One of the old-timers will probably be able explain how it would be done with more primitive tools. --tcsetattr (talk / contribs) 06:16, 13 September 2008 (UTC)

Graphing calculators are great for getting a quick rough idea of what a function does and finding out roughly where the axis intercepts are. Once you've got that, it's much easier to know what you need to do work things out more precisely (for example, you know how many intercepts there are so you know when to switch from finding more to proving there are no more). I can't think of anything that absolutely requires a calculator, but it is much quicker that working it out analytically from scratch, of plotting it by hand. --Tango (talk) 08:23, 13 September 2008 (UTC)

Reading this thread, I was also puzzled by which part of pre-calculus actually requires a graphing calculator, as opposed to it being a handy convenience tool. Digging around a bit, I found this question paper from this pre-calculus course outline, which includes the following question:

“ Use your graphing calculator to sketch the graph and label the vertex, y-intercept, and x-intercepts:

1. y = -2(x + 3)² + 7
2. 4x + y – 2x² = 9

”

IMHO, the student who algebraically determines the co-ordinates of the vertex and intercepts and confirms these by sketching the graphs by hand has actually learned something about parabolas, quadratic equations and how graphs change under certain linear transformations of co-ordinates. But the student who follows the instructions, copies a graph from the screen of their graphing calculator, and reads off and writes down the approximate locations of the vertex and intercepts has only learned how to use a graphing calculator and has learned little or no mathematics. It is a perfect example of a problem where the route to the answer is more important than the answer itself. Gandalf61 (talk) 11:41, 13 September 2008 (UTC)

That's a question intended to test your ability to use a graphing calculator. If that's specifically on the sylabus, presuming they expect you to need to know it later. Judging by the name, I expect pre-calc is meant to prepare you for calculus - you don't need a graphing calculator for any calculus course I've done... --Tango (talk) 13:47, 13 September 2008 (UTC)

No no no, pre-calc has absolutely nothing to do with Calculus nor does it prepare you for Calc (don't ask me why they call it pre-calc, I don't know). I'm guessing you don't have pre-calc in UK or where ever you are from, but it's here in America. Pre-calc is basically the study of functions, graphs, and advanced algebra. ScienceApe (talk) 17:38, 13 September 2008 (UTC)

...and how to use graphing calculators, apparently ;) Gandalf61 (talk) 21:08, 13 September 2008 (UTC)

Early pocket calculators were expected to be used for hard stuff like 34201·4837, but actually they are used for computing 3+18, which is no longer done by hand. Teachers expect students to use graphing calculators for sketching y = −2(x + 3)² + 7, but probably it is used more for sketching y = 2 and y = x and the like. Bo Jacoby (talk) 13:36, 13 September 2008 (UTC).

In the past before learning calculus a student would just have to plot each y point for different x values. They would then learn as part of the calculus course how to find the minimum and maximum points and possibly inflexion points which would make sketching the graph and finding the zeros much easier. Dmcq (talk) 14:42, 13 September 2008 (UTC)

I certainly did that during my A-levels, 3 or 4 years ago - maybe it's just the US that teaches using graphics calculators rather than actually plotting graphs. (I did have a graphics calc for my A-levels, but I don't remember using it very often.) --Tango (talk) 14:45, 13 September 2008 (UTC)

Here in Ontario, Canada, we learn to graph lines, parabolas, and high-order functions by hand in grades 9, 10, and 12, respectively. Graphing calculators are sometimes used for advanced algebra because the other steps involved are more important than solving the zeros of an equation like y=2x^5+3x^4-23x^3+9x^2-9x+200.

I'm assuming that pre-calculus corresponds to Ontario's advanced functions course, which is about high-order polynomials, continuity, zeros, asymptotes, and the like. Advanced functions is a pre-requisite for the calculus & vectors course, so in this sense it can be termed "pre-calculus". --Bowlhover (talk) 03:13, 14 September 2008 (UTC)

(American, currently undergraduate.) I can't really speak for the effectiveness of a particular Pre-Calc course, but the purpose of precalculus is to get you ready for calculus by introducing or reviewing things you'll need to know about, like limits, the transcendental functions, and basic use of cartesian coordinates. If it's been decided you'll need to be able to use a calculator in calculus, that's a reasonable tool to teach the use of in precalculus. It can't replace any of the other knowledge you'll need, other than the use of older tools like log tables, but it's not an unreasonable thing to put a little time into, just to make sure everyone's on the same page. Most of the things I've used a calculator for in school involved precise calculations that couldn't be conveniently done by hand, in answer to questions like, "What is the measure of angle A to three significant digits?" or "What is the determinant of this matrix?" Neither of those makes use of an advanced calculator's graphing, approximation, or symbol manipulation capabilities, and no question a national test will ask does either. If you can't do it with a scientific calculator and some thought, it shouldn't come up. I remember teachers using the displays of graphing calculators to teach theory, since it's nice to have a fast and accurate picture of what you're learning about, but that doesn't come up on a test. That still doesn't explain the ubiquity of the TI-83 in our curriculum, which I blame on secret kickbacks from calculator distributors. Black Carrot (talk) 06:16, 14 September 2008 (UTC)

One other thought, on rereading the second Original Post. It's not entirely outside the realm of possibility that your teacher isn't actually good at math. Just something to think about. Black Carrot (talk) 06:19, 14 September 2008 (UTC)

So we seem to have reached the conclusion that the parts of a pre-calculus course for which you absolutely require a graphing calculator (rather than just a numerical scientific calculator) are just those parts that teach you how to use a graphing calculator. Yes ? Gandalf61 (talk) 08:20, 14 September 2008 (UTC)

No, I don't think so. The professor said parts of the exam require the use of a graphic calculator. ScienceApe (talk) 14:17, 14 September 2008 (UTC)

Since you failed to provide an example of a question that can't be answered without the graphing calculator (and the only example given by anyone else was "use your graphing calculator to do something that's already easy enough to do with pencil and paper alone") you forfeit the right to object to the conclusion. --tcsetattr (talk / contribs) 20:17, 14 September 2008 (UTC)

No, the professor really did say that. If you don't believe me, well that's your problem I guess. I didn't provide an example because we haven't gotten to those kinds of problems yet. The rest of your post is silly and absurd. Saying you forfeit the right to do anything is childish at best, rude at worst especially on the reference desk. I suggest you keep that kind of talk off of here, it's not civil. ScienceApe (talk) 03:19, 21 September 2008 (UTC)

Before graphing calculators they used common sense (except for people who didn't use common sense). Look: If you don't understand graphs of polynomials, rational functions, exponential and logarithmic functions, etc. without a graphing calculator then you don't understand, and a calculator won't change that. Calculators are not supposed to be a substitute for using your head. Nor are they supposed to be an anesthetic. Michael Hardy (talk) 23:13, 14 September 2008 (UTC)

Excuse me? I never made a claim that calculators replaced "using your head". You're arguing a strawman here it seems. My professor said there were functions that would be impossible to graph without a calculator, even for people with complete knowledge of functions, polynomials, logs, etc. I was curious to know how they graphed such things before calculators. From the responses here, I presume they simply didn't graph such complex problems. ScienceApe (talk) 03:28, 21 September 2008 (UTC)

Also graphing a real function on a desktop computer was available like a decade before graphing calculators were. If you're asking a question on this refdesk, then you likely have access to a computer powerful enough to graph at least simple functions.

Let me also mention that apart from graphing calculators, we have (surprise) calculators with text-only or numeric-only screen. These are much cheaper and were also available a decade earlier, and you can use these to do calculations as well. You can even use them to graph a function with the help of a graphing paper and a pencil. – b_jonas 16:32, 19 September 2008 (UTC)