Wikipedia:Reference desk/Archives/Mathematics/2009 October 3

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

October 3

Calculator

The number pattern on mine has the 1, 2, 3 at the bottom and the 7, 8, 9 at the top. Now on my phone it is the opposite 1,2,3 at the top and the 7, 8, 9 at the bottom. Why is this? It obviously leads to mistakes. I am certain there would be less pissed off people answering wrong numbers and almost-graduates who managed to flunk out of school due to this mismatch. What gives? 174.152.243.23 (talk) 00:09, 3 October 2009 (UTC)

The dial phone came first, with had letters corresponding to numbers, and when phones went "digital" with tone dialling buttons they logically put ABC before WXYZ, but meanwhile Texas Instruments had brought out their calculator with higher numbers at the top, and computer keyboards followed with the same arrangement. I have to mentally adjust every time I dial a number on a phone because I learnt to "touch-type" on a calculator. Dbfirs 01:18, 3 October 2009 (UTC) Thanks to Anonymous for pointing out (below) that the calculator arrangement is over a hundred years old. Dbfirs 17:23, 3 October 2009 (UTC)

See also the article on numeric keypad: "The arrangement of digits on numeric keypads is different from that of telephone “Touch-Tone” keypads — this may be confusing for those who use one of these arrangements more often". The wording "may be confusing" is an understatement. It is downright irritating. Bo Jacoby (talk) 03:38, 3 October 2009 (UTC).

I don't think I have problems with this. I do the keypad on the keyboard with all 5 fingers. I dial my phone with 1 finger, my thumb. Maybe that's why. StatisticsMan (talk) 04:31, 3 October 2009 (UTC)

I don't have problems with it either and you may have found the reason - I don't tend to use to use multiple fingers on a keypad or any kind, but I use my middle finger on a calculator/computer keyboard and my thumb on my phone. --Tango (talk) 05:27, 3 October 2009 (UTC)

I might be wrong about Texas Instruments (theirs was the first pocket calculator I saw around 1972, and it was very expensive, certainly well beyond my means!), but did Sanyo produce one in Japan before then? I'm trying to remember whether any of the electro-mechanical calculators that I used around 1970 had a layout of numbers like a modern calculator. My recollection is that they didn't. The ones I used didn't, but some did!

My confusion with layouts arises because I tend to use the same fingers for both layouts, but I have to concentrate harder to dial a number on a phone, and yes, it does help to use just one finger. Dbfirs 07:52, 3 October 2009 (UTC)

You guys are too young! The "calculator-style" numeric keypad goes back to mechanical adding machines. According to this page, this machine was the first to use it and was first produced in about 1912 or 1914. Nobody worried about this when the phone keypad was designed because phones were meant for the general public whereas only a few people, such as computers, would make heavy use of adding machines. And, as noted above, people wouldn't like it if the phone company messed with the alphabet. --Anonymous, 10:28 UTC, October 3, 2009.

Hard to figure how this wound up in the Math page, but whatever. It's important to note that the original arrangement of the numbers on adding machines and dial phones were both done for practical reasons. Numbers in a calculator are entered left-to-right, and 0, 1, etc., tend to be more common in the high-order digits, hence they are closest to the user. Dial phones, which were clearly constructed with right-handers in mind, are pulled clockwise to generate the pulses, so naturally the 1 was closer to the finger-stop. 0 was put last, as it was used to suggest "O" for "Operator", though not to be confused with the M-N-O over the 6. The letters were originally connected with exchanges, long before exchanges became all digits and 800 numbers co-opted the letters to make clever mnemonics. And as noted above, because of the association of letters with numbers, the touchtone phone put 1-2-3 at the top instead of the bottom. However, both phones and calculators still have 0 at the bottom. There are also calculators with extra keys for 00 and 000, for further entry convenience. Touchtone phones had the * and the # keys from the beginning, although it was awhile before they were used very much. →Baseball Bugs ^{What's up, Doc?} carrots 11:45, 3 October 2009 (UTC)

Calculator is a math device so the math page could easily be the first place someone would think to ask such a question. StatisticsMan (talk) 19:39, 3 October 2009 (UTC)

The original use of "0"=Operator, surely does not explain the position of 0 on the dial. The dial emits pulses down the line to the exchange, according to the distance the dial travels in returning to home base. Dialling "1"=1 pulse, "2"=2 pulses, etc and "0" produces 10 pulses. [Obviously there is no such thing as zero pulses.] The digit "0" therefore belongs after "9" on the telephone but before "1" on a calculator (and also on the numeric keypad on a PC). Sussexonian (talk) 20:55, 4 October 2009 (UTC)

Calculator (solution)

What solutions are available for the above? It seems that all are in agreement that the above key arrangement is unacceptable.

1. I still have my Ma Bell touch tone desk phone ( I think I have a wall model boxed up in the basement as well). I plan on opening it up and reconnecting the DTMF connections for the 1st and 3rd rows of buttons. I can then use white out and get the number pad back in the correct order.
2. This won't work for phones with newer/smaller/unmodifiable circuitry. I am thinking that the phone companies could reconfigure their switches (as to how they process the DTMF). Possibly stickers could be passed out to relable all of the existing phones.

This might seem like a lot of trouble, but I am sure that there would eventually be a payoff from the resulting increase in efficiency. 70.4.71.74 (talk) 11:01, 3 October 2009 (UTC)

That's an interesting idea. But do you really use the phone and the calculator both heavily? Usually someone using a calculator (or the numeric keypad on a computer keyboard) is doing a large amount of data entry - dozens of numbers per minute, let's say. How often do you make a phone call? →Baseball Bugs ^{What's up, Doc?} carrots 11:50, 3 October 2009 (UTC)

I already gave a solution above, and Tango backed it up. Do each of the two in different ways. I use my full right hand to use the computer number pad with starting position thumb through pinky on 0, 4, 5, 6, and enter, respectively. I have also practiced typing this way to gain speed a long while ago. If I dial a cell phone, I hold it in my hand and use my thumb of that hand only to dial. If I have a landline phone that is bigger, I might do that or I might hold it in my left hand and dial with my pointer finger of my right hand. It's a completely different method so I don't get confused. Or, perhaps the solution is because I have practiced both. I don't know why, but for me this isn't a problem at all. StatisticsMan (talk) 19:32, 3 October 2009 (UTC)

A guy could obviously rewire his own home phone to match a calculator, but that might give him even more trouble when he goes out into the world and all the phones are at odds with his. And how would you rewire a cellphone, for example? Data entry people have a method, as you do, for typing the number pad quickly, a skill which also works for calculators (and vice versa). I'm trying to figure out why on earth someone using the telephone would ever need to enter numbers at such a fast and voluminous rate as with data entry. Maybe telemarketing? But they might well have VOIP, in which case they could use the keyboard number pad anyway. It makes more sense to simply learn one skill for one operation and another skill for another operation. It reminds me of some who fear driving because they might hit the accelerator instead of the brake. Well, you simply train your mind that when a braking situation arises, or a traffic slowdown, or anything unusual, you remove your foot from the accelerator. Practice makes perfect, or at least makes "permanent". →Baseball Bugs ^{What's up, Doc?} carrots 20:14, 3 October 2009 (UTC)

I think telemarketers don't even dial. I think they have a list of phone numbers in a computer and the computer dials. However, I am not sure on this. And, I agree that it's probably not necessary to dial at extreme speeds. StatisticsMan (talk) 04:52, 4 October 2009 (UTC)

Rectangle under pinhole projection

I have an image of a rectangle under pinhole projection of unknown parameters. Can I solve the rectangle's aspect ratio? --194.197.235.240 (talk) 16:15, 3 October 2009 (UTC)

In liner optics it's identical to this of the original rectangle.--Gilisa (talk) 19:47, 3 October 2009 (UTC)

Afraid not, the cross ratio you get from joining opposite corners and projecting lines will be the same as for a square. You can project a rectangle onto a square. Dmcq (talk) 20:13, 3 October 2009 (UTC)

If the line on which the the pinhole camera and the center of the square are located on is vertical to the rectangle plane then we can follow the simple solution of linear optics. --Gilisa (talk) 07:06, 4 October 2009 (UTC)

If the original rectangle and the projection are on parallel planes, they have to be similar. If the planes aren't parallel then opposite sides of the projected quadrilateral won't be parallel and you can calculate how far off from parallel the two planes are, so you have all the information you need. I don't see how a non-square rectangle could ever be projected to a square. Rckrone (talk) 22:29, 3 October 2009 (UTC)

Correct me if I'm wrong, but I think projecting a non-square rectangle to a square is really easy if the two planes are not required to be parallel. Michael Hardy (talk) 22:33, 3 October 2009 (UTC)

I'm still not seeing it. I think you're right it would be possible to project both to the same quadrilateral (but the quadrilateral won't be a rectangle), so I am wrong about that. However, if in addition to your projected shape you also know where the pinhole is, I think you have all the information you need. Rckrone (talk) 23:18, 3 October 2009 (UTC)

I seem to recall a theorem of elementary geometry stating that any rectangle at all can be realized as the projection of a square from a point. If so, the shape of the rectangle would not give enough information to determine the aspect ratio: it could be a square, but other rectangles would also have irregular quadrilaterals as projections from a point. Michael Hardy (talk) 22:32, 3 October 2009 (UTC)

I'm reversing what I said originally to agree a bit with Rckrone. You can't get to a square directly with a projection except with an infinitely long projection. If you know the distance from the pinhole to the projection then yes measuring that ought to give you the original aspect ratio. If you don't know the relationship between the pinhole and the screen then no you won't be able to calculate the original aspect ratio. Dmcq (talk) 10:42, 4 October 2009 (UTC)

Thanks --194.197.235.240 (talk) 20:27, 5 October 2009 (UTC)