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All you need is...

a cheap, small, portable computer

. . . . . . . but is the Texas Instruments TI-92 the answer?

Our premise: Teachers and students need time and reasonably unlimited access to software in order to master it and put it to productive use. They cannot be expected to buy computers for themselves, even with prices coming down below £1000.

What's needed: Access for schools and colleges to extremely cheap, small, portable versions of their own computer system which their teachers and students can take home. In particular the machine should use the same interface (point & click - WIMP as we used to call it) and have the same software.

Lap-tops (PC, Mac or Archimedes) do meet most of what's needed. You can install your own software. You can take home the school spreadsheet, word processor, logo, interactive geometry package, etc etc, and get to grips with it. The problem is lap-tops are just so expensive. A colour "notebook" may cost as little as £850 but no school is going to allow such hardware to be borrowed by students. Do we really need the colour though? Not really, not at home, when you're not trying to keep the attention of multiple-sensations-per-second TV-addled youngsters. If expense lies mainly in the quality of the screen, then make it black and white and bring the price right down

The contender: The Texas Instruments TI-92

What is the point of a gadget which does not meet what's needed at all? It isn't cheap enough. It isn't a computer (OK you define what a computer is). It is a calculator, but then we still haven't fully sorted out the place of calculators in schools either. There's no mouse. It's small, which is what we want, but then this means that the barrage of necessary key-pressing sequences require the fingers of a concert pianist. And there's a lot of advertising about it in the educational press too. Is the TI-92 really the next big thing in information technology in schools? Is it really going to achieve our aim? Or is it actually a backward step?

Don't get me wrong, this isn't a diatribe against Texas Instruments. My mathematics department is committed to the TI-82 calculator and we strongly recommend all our senior students to buy one.

It is simply that a small non-mouse non-conventional-windows gadget that costs just too much (although you do get Derive and Cabri) is not what is needed. And when it comes to Derive, let's face it, there's no real place for Derive in schools - despite all the research and academic interest. A-Level isn't difficult enough to need it. Other than as a magic black box that finds answers to otherwise uncalculable problems, Derive is a red herring (white elephant?) Cabri may be OK now. The first version was neat and initially fascinating but somehow too unfriendly given limited access time in schools. Now, it could be as good as Geometry Inventor or Geometer's Sketchpad. A small plus then for the gadget!

You may say what's needed isn't available, so let's make do with what is. No. Consider the Internet. It offers immense potential to schools. Resources, information, downloadable files, communication, and (whichever of Netscape or MS Explorer triumphs as chief browser) the Windows interface rules. Hardware must be Windows compatible. Student's are not going to venture out into the wide world from the safe haven of school to encounter industrialists, managers, decision makers, opinion formers or anyone else, carting round that little black box gadget.

What is far more likely, and more exciting, is that manufacturers will be developing a lap-top which is "Internet-Ready", meaning that it will get its software from the Net via what is being called a Network Computer (NC) standard. Interest is already being expressed in the press. In the near future you will buy a terminal, take it home and plug it into the software you choose. Schools will presumably have a licence, including home use, to cover this.

A plea to hardware manufacturers out there: Make a cheap Windows lap-top for educational use, powerful enough to run Word and Excel (and therefore anything else). Perhaps make it totally dependent on the school system (no disk drive just a link cable?) or on the Internet. Make it black and white if necessary. Work to get the price way down below £200 and you'll clean up.

Numbers in Words

[From ATM's magazine, Mathematics Teaching, March 1996]

In the back of my stock cupboard I recently came across an old copy of Mathematical Pie, dated October 1960, issue 31. Under the heading Numbers In Words, this problem appeared:

The eight letters in FORTY SIX are different but this is neither the largest nor the smallest number that can be expressed in words in which all the letters are different. What are the largest and smallest numbers that you can find expressed in words in which all the letters are different?

I was intrigued and thought it might have the makings of a puzzle for my Monthly Maths Puzzle which I set for the whole school to enter, first prize a £5 gift token. My interest was increased when I discovered issue 32 in the cupboard as well and found that it contained no solution to the problem. So, the Monthly Maths Puzzle was decided. The poster was put up and over the next month the entries trickled in.

Lowest number
ZERO was soon submitted. Zero seemed the obvious choice for smallest number and a lot more zeros came in. And then came MINUS TWO! A sixth former's submission argued that negatives did not count as they were only large numbers seen from a different viewpoint, but I disagreed. Then I received MINUS FORTY and this remained unbeaten till the end.

Largest number
FORTY SIX was beaten by SIXTY and then by EIGHTY, and then, as is often the case in puzzles of this kind, one number seemed to be coming from all directions, year 8 and 9 pupils particularly. This was THOUSAND. The sixth former who had argued against negatives was arguing here in favour of what he called Loschmidt's number, which I hadn't heard of, but which has the value 2.7 x 10²⁵.

Of course the words include two m's and s's but he got round this by claiming it was normally known by the abbreviation NL. Not in the spirit of the competition I thought. A boy in Year 9 who is often amused by maths though he finds it academically rather bewildering, approached his form tutor with a suggestion. For some reason (I suppose he imagined he was really onto something) he chose to whisper his largest number into the teacher's ear. "Infinity," he whispered proudly. "Three i's," the teacher whispered back. Another pupil entered anonymously the German for infinity, which is UNENDLICH. Anonymity was clearly a good ploy. THOUSAND was to be beaten though, as there was another rush of entries, this time of FIVE THOUSAND, and with one pupil explaining laboriously that MILLION, BILLION and so on weren't going to work, it seemed now that the problem was solved. I had many entries of both minus forty and five thousand too. We teachers were convinced. We were surprised therefore to receive FORTY CUBED from a Year 11 pupil. This reopened the problem. It definitely seemed non-trivial now. We spent the occasional lunch time trying to dream up calculations which would beat forty cubed (64000). The use of "squared" had potential but the s and the e caused problems. We were beaten anyway by the same pupil (and another from Year 8) who came up with SIXTY CUBED (216000). A teacher produced ALEPH TWO, one of Cantor's endless sequence of transfinite numbers, but this seemed unfair though I couldn't exactly say why. As far as the pupils were concerned it looked like minus forty and sixty cubed were going to claim the £5, and then, virtually on the last day of the month, that same Year 11 pupil came up with more. Being short of cash, she'd spent some of Half Term looking in her calculator guide book and pressing buttons and was now offering SINH FORTY CUBED which weighs in at 1.63 x 1051, that is if you take it to mean (sinh 40)³. She'd also considered sinh 40³ but wasn't sure as it was too big for her calculator to handle and bigger therefore than 1099. In any event, the £5 was hers.
So there you have it. Any advance on MINUS FORTY and SINH FORTY CUBED?

A recent offering from Tom Lynn:
Just thought I'd throw in my best shot for smallest number for the "numbers in words" article. Assuming I can't have MINUS ALEPH FORTY, I reckon that MINUS EXP FORTY will be pretty hard to beat.

A spreadsheet's largest number

What is the largest number your spreadsheet can display?

It may appear that all this problem requires is the entering of increasingly large numbers until the spreadsheet complains! However, many spreadsheets will accept very large numbers so this trial and improvement approach is inadequate. A better method is to use the spreadsheet itself to create these larger numbers. Enter a large number in cell A1, then in A2 enter A1*1.1 and copy this down the column. Sooner or later the spreadsheet will display ERROR or #NUM! In the first cell that does this, change the multiplying factor from 1.1 to 1.01 and continue as before. At the next error, change 1.01 to 1.001, and so on.

The accuracy that Excel uses for display can be maximized by selecting Format... Number and choosing Scientific in the Category Window.

Then the accuracy can be increased by adding zeros to the Code, i.e., alter 0.00E+00 to read 0.00000000000000E+00. It is different in other spreadsheets, for example, to maximize the accuracy in Sparks, the options are more limited. Select Looks... Number format. Then choose Decimal places: 9, and Scientific.

With Excel 4 running on an old PC, the largest number I got was
1.79769313486231 x 10³⁰⁸
However, if the multiplying factor is entered as (1+ 10^(-15)) instead of 1.000000000000001 then the final digit can be increased from 1 to 2. In some other spreadsheets, the solution may not be so straightforward. Some behave a little erratically when the numbers get big.

Can time be metricised?

by Zaini Ismail (Zyne), Singapore

If so, how and what are the possible consequences? I hate to work with 7,12,24,60,52,365,366 and 3600. Can we have something like 10 millizeconds=1 centizecond, 10 cz=1 z, 1000z=1 kz, 1000 kz=1 zyne and so on, so that calculations of time can be done justby shifting decimal points. As this is something new, I hope fellow world mathematicians, scientists and astronomers will take it up as a challenge for there is nothing impossible in this world. What we think fiction centuries ago, are now becoming reality and what we think absurd now shall become reality the next millenium. So a challenge indeed. That's why I prefer naming time in 'zynes' taking after my name 'Zaini'. This idea has been growing on me since I was a seven year old kid for I preferred to work with ones and zeros just like computers are now doing.

Thanks for reading this original idea. It has been daunting in my dream. If we could think harder, the future would be much easier.

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