PDA

View Full Version : OT: A question for skilled mathematicians, or am I just thick?



Billy T
04-02-2003, 01:16 PM
Hi Team

I need a hand with a mathematical problem. I'm OK on most routine stuff but my maths education finished in in the 60's and this has me stumped.

I have a series of formulae for calculating particular electrical characteristics at varying frequencies including some worked examples (minus the actual working unfortunately). The actual characteristics are unimportant, it is the means of obtaining the result that I can't fathom.

The formulae include a decimal fraction i.e. 0.247 or 0.5 in superscript after the number in the same way that we might write a power. Problem is, I haven't the faintest idea how the superscript number is applied and even my fairly switched on daughter (who just passed fifth form NCEA maths while still a 4th former) can't help. All she can do is laugh at my struggles with all the sensitivity that we have come to expect from children when they finally realise that not only do their parents not know everything, sometimes they know nothing at all! :(

Here are a few examples with the final result included.

3454f (0.753) = 1733 [where f= 0.4, and (0.753) follows f in superscript and without the curved brackets]

9.06/f (0.247) = 11.4 [where f = 0.4, with 0.247 as in the example above]

The value f is the frequency in MHz and the examples given above are for a frequency of 400 kHz.

A couple of example for a superscript factor of 0.5 are:

44f (0.5) = 2147 where f = 500MHz

0.118f (0.5) = 5.7 (f is again 500MHz)


I want to solve the following examples for f = 350 kHz

3454f (0.753) =?

493f (0.753) =?

9.06/f (0.247) =?

4.13/f (0.247) =?


Obviously the decimal fraction is a power or factor of some sort but I'm not even sure that description is correct. I'm picking that a scientific calculator is required for this and I have one right in front of me now, but the problem is I can't drive the thing apart from a few very basic functions.

Any help will be gratefully accepted.

Cheers

Billy 8-{) Imagine emoticon for face full of hope here:.........


Oh how I wish I'd paid more attention in maths all those years ago :( :(

Horses Hoof
04-02-2003, 01:25 PM
I wouldn't know either. I'm the village eejit

Graham L
04-02-2003, 01:34 PM
What are you calculating? The forms you give don't seem like anything I have seen.

A superscript "0.5" means square root, "0.25" would be fourth root.

There is often a factor of "2 pi f" in electronic calculations: that gives the "omega" term -- radians/sec . As in XC=1/omega.C, and XL=omega.L . Sometimes the "2 pi" is calculated ouit and given as 6.28(etc) or even as the reciprocal ... delay while he pulls out the slide rule ... approximately .16 .

I don't know whether to be ?:| or :_| or :O

roofus
04-02-2003, 01:40 PM
Eeasy peasy japanese

ok lets look at this equation

3454f^.753 where f= 0.4

The thing to remember is that you must work out f^.753 first
so 0.4^.753 = 0.502
then times this by 3454

3454 x 0.502 = 1733

Now i don't want to solve them all for you, otherwise that would destroy the fun :-)

Horses Hoof
04-02-2003, 01:43 PM
Fecken hell, where did you guys get your brains. Can I get one too

Billy T
04-02-2003, 01:45 PM
I feel better already Graham :)

The formulae are taken directly from a New Zealand Standard, and the first complete example yield a field value of 1733 Volts per metre, and the second a field value of 11.4 Amperes per metre.

The more I tried the confuseder I got :8}

I might play with with the possible square root example and see what happens.

Cheers

Billy 8-{) :D

-=JM=-
04-02-2003, 01:53 PM
The button your after is x^y in the case of the windows scientific calulator.

or will be x with a superscript y above it.

Those buttons let you do 'to the power of'

Billy T
04-02-2003, 01:54 PM
Thanks Roofus, but what does the ^ represent?

One or two clearly worked examples suitable for somebody who spent too much time asleep in maths classes would be a real help:8}

Cheers

Billy 8-{) :|

roofus
04-02-2003, 01:55 PM
>
> The more I tried the confuseder I got :8}

Interesting, you learn a new word every day :-)

roofus
04-02-2003, 01:56 PM
>
> The more I tried the confuseder I got :8}

Interesting, you learn a new word every day :-)

roofus
04-02-2003, 01:59 PM
the ^ is to the "power of"
But has graham said when you have a "power of" that is a fraction then it becomes a square root. But i don't know what the computer uses to represent square root. In excel you type "sqrt"

roofus
04-02-2003, 02:05 PM
> I want to solve the following examples for f =
> 350 kHz
>
> 3454f (0.753) =?
.35^.753=.453611
.453611(3454)=1566.771

> 493f (0.753) =?
.45611(493)=223.63

> 9.06/f (0.247) =?
.35^.247=.7716
9.06/.7716 = 11.74

> 4.13/f (0.247) =?
4.13/.7716 = 5.3526
>
> Obviously the decimal fraction is a power or factor
> of some sort but I'm not even sure that description
> is correct. I'm picking that a scientific calculator
> is required for this and I have one right in front of
> me now, but the problem is I can't drive the thing
> apart from a few very basic functions.
>
> Any help will be gratefully accepted.
>
> Cheers
>
> Billy 8-{) Imagine emoticon for face full of hope
> here:.........
>
>
> Oh how I wish I'd paid more attention in
> maths all those years ago :( :(
>

Susan B
04-02-2003, 02:29 PM
>> I want to solve the following examples for f =
>> 350 kHz

>> 3454f (0.753) =?
>.35^.753=.453611
>.453611(3454)=1566.771


So to get the answer to this with a Casio fx-82TL scientific calculator (standard school issue) I did this:

.35 then press the x button with the y superscript on it, directly under the Off button .753 = 0.453611 x 3454 = 1566.771

Easy peasy. :-)

Now, what did you say it was for? :p

Why is my reply in bold? I have no bold formatting tags.

Billy T
04-02-2003, 02:39 PM
EUREKA :O

I did it, and with the scientific calculator too B-)

Now I can grab previously mentioned smartypants daughter when she gets home from school and show her something mathematical I know that she doesn't ]:)

Thank you Roofus; once again PF1 shows it's colours as the premier forum for questions on just about any topic.

Cheers

Billy 08-{) :D :D :D

Never give up Horses Hoof. Next step up is the Horse's **se
and before you know it you'll be a Horse's Head :|

Billy T
04-02-2003, 02:48 PM
You were a fraction too late Sis :x

I just found my way around my Casio fx-82TL scientific calculator (snap) and produced the correct answer.

The world can sleep easy tonight knowing that the sum total of knowledge in the universe has just been increased by ^ B-)

Cheers

Billy Bro O8-{) :D

Like the halo? :8}

rugila
04-02-2003, 03:01 PM
Try a bit more, just for fun and maybe ejermakation.
The expression x^y is short for “x raised to the power of y”. The number y is also called an “index” (plural is indices, unlike plural of the index in your book, or the infamous consumer’s price index etc which are indexes).
y can be any number, positive, negative or zero. (x^0 always equals 1, no matter what x is, and x^(-1) is the reciprocal of x (that is, 1/x).
If y is not a whole number (say its fractional) this raises some very interesting questions. Ask Excel say to calculate say (-2)^(0.5) and it gives the Excel equivalent of “don’t be silly”. But you’re not being silly and this sort of thing actually (in addition to having two answers, not just one) actually plays a very interesting role in electrical circuitry.
If you have something like 2^0.345 Excel etc will give you one answer whereas actually there may be quite a number of valid answers.
This sort of stuff is all good clean fun.
Fortran used x**y for x^y, currently Excel calculates x**y = x*(10^y) , whereas Visual Basic gives the Visual Basic equivalent of “don’t be silly” if you try x**y.
Before modern computers and calculators, the only feasible way to calculate x^y (other than in the simplest cases) was by logarithms, which were concepts invented by Briggs and Napier about 1600 for this sort of thing as well as to make multiplication easier.
Rather than look up logarithm tables for their calculations of x^y etc., some mathematicians such as Karl Gauss and Zacharias Dase used to memorise the tables, effectively carrying tables of logarithms around in their memory for instant calculation(I don’t know to how many decimal places). Multiplication was easy to them, Dase (lived about 1770) could multiply two 10 digit numbers in his head and give the correct answer within about 5 seconds.
People generally didn't bother retaining this ability (apart from parlour tricks) after the advent of modern calculators, and of course computers.
(a) none of the above came from Google or other search engine
(b) anything more you want to know?

Billy T
04-02-2003, 03:27 PM
There have been some great brains out there alright rugila. Apart from the odd idiot-savant with narrowly focussed powers, there have been some quite normal individuals with fantastic mathematical powers.

I seem to remember there was an Indian? gentleman around in recent times who could beat a computer to some answers, but even if not that fast, he could match a computer for accuracy and was probably more accurate than a pentium with the floating point error.

Then there was me :(

Cheers

Billy 8-{) :| I think I'll go and have a lie down

Heather P
04-02-2003, 03:37 PM
Cheer up Billy,

My daughter is doing a Uni maths paper (summer school, another week to go). I made the mistake of peering over her shoulder last night as she was working on a number of problems.

Vaguely recognised the bracket things she was working with as a dim, dark distant memory but hadn't a clue what they were for - 2 numbers side by side, another pair below them and big brackets around all four.
???

I thought (briefly) about asking but figured the answer would probably require an asprin or two so departed rapidly.

At least I can still beat her at scrabble!

Graham L
04-02-2003, 03:44 PM
That's matrix stuff, Heather. Very clever. I have programmed some of this (simple only) for graphics transfomations, once upon a time. I've forgotten it all. :D

Heather P
04-02-2003, 03:56 PM
Matrix. That also rings a very distant bell but I still can't remember what they were for. Actually, maths was my best subject at school but it's the old story of "Use it or Lose it".

My mathematical streak has turned into more of a logic streak. Complex formulaes these days start headaches so I try to avoid them. Logical processes on the other hand...

<* sets off to sort a pile of papers into a logical order in order to make sense of a problem /*>

rugila
04-02-2003, 08:53 PM
Heather P. How can you beat your daughter at scrabble if you use words like formulaes?

Heather P
04-02-2003, 08:55 PM
I cheat!

rugila
04-02-2003, 08:57 PM
And as for matrices, these have (among other things) very useful application in the design of electric circuits, which were what I think motivated this thread in the first place.

Heather P
04-02-2003, 09:01 PM
OK, just checked the dictionary.
formula (pl. -ae, -as)

So does this mean I was right twice or wrong once or wrong twice? (Seeing as how this is a maths question) ?:|

rugila
04-02-2003, 09:12 PM
Heather: You're baiting me.
Formula is an old word from Latin (which has been a dead language for centuries.
Plural of Latin words ending in -a was -ae, like mensa (=table) mensae (=tables), these was no -s plural in Latin.
English speakers generally like their plurals with -s, so they tend to like formulas, whereas some of the stickers to tradition prefer formulae. Either is acceptable in modern English as your dictionary indicates.
Formulaes is one word=one error = not in any dictionary of which I am aware.
PS I never was a schoolteacher - they didn't like my ideas and wouldn't have me.

Heather P
04-02-2003, 09:23 PM
Me? Bait people? Surely not! ;)

The problem with a wide and varied vocabulary. Sometimes I fool even myself.

Elephant
04-02-2003, 09:25 PM
OK, just checked the dictionary.
formula (pl. -ae, -as)
So does this mean I was right twice or wrong once or wrong twice? (Seeing as how this is a maths question)

Fomula is ONE of them.

Formulae and / or Formulas or More that one.

Formulaes does NOT compute. :-)

Means you were just wrong ONCE!!!!

Heather P
04-02-2003, 09:29 PM
Ah Elephant,

Sometimes it is far more fun to be spectacularly wrong by being wrong twice rather than just a mere once.

Being wrong just once is really quite tame.

Are you sure?

Billy T
04-02-2003, 09:41 PM
An interesting thought Heather?:|

To my mathematically challenged mind, maths and logic go hand in hand, yet although I cannot fathom maths, I earn my living as a diagnostician, which requires a very logical mind with just the occasional flight of fancy for a left field solution.

Maybe I just should have stayed awake in class a bit more :8}

Cheers

Billy 8-{) :|

rugila
04-02-2003, 10:17 PM
What does a diagnostician do? Is that medical diagnostics? Or some other type?
The extent to which mathematics is logical and/or vice versa has been the subject of some dispute. Basically they just both do their own thing and don’t entirely coincide.
Around 1890 the German logician Gottlob Frege published (after many years work) his attempt to put all arithmetic (which is the totality of what computers do apart from making noises, having bugs, taking up space and using power) on a consistent logical basis. Not many years later Bertrand Russell totally demolished Frege’s thesis with a two-line paradox.
Some years later (1930’s) the Austrian logician Kurt Godel proved that some pseudo-logical systems (including elementary arithmetic and thus including computer arithmetic) contained valid propositions that could not be proved valid or invalid within the system itself, and were thus not logical in this sense at least.
Most of our modern logic comes from the Greek Aristotle, after whom we tend to automatically accept obvious but not necessarily valid fundamental premises such as “what is true cannot be false” and similar.
This sort of stuff has been challenged by a variety of thinkers such as the American CS Pierce (he pronounced his name as “purse”, does Google tell you this?) who developed a “three valued” logic as an antidote to Aristotle’s two valued version.
Why am I writing this stuff anyway?
What did you say diagnosticians do, and why do they need to be logical?

DangerousDave
05-02-2003, 07:01 AM
ARGHHHH its 5th form physics all over again!!!!!

:P lol

- David

Horses Hoof
05-02-2003, 07:40 AM
> I seem to remember there was an Indian? gentleman
> around in recent times who could beat a computer to
> some answers, but even if not that fast, he could
> match a computer for accuracy and was probably more
> accurate than a pentium with the floating point
> error.
>
> Then there was me :(
>
> Cheers
>
> Billy 8-{) :| I think I'll go and have a lie
> down

I can beet a computer too, if I work out the answer, before I put the question in the computer

Billy T
05-02-2003, 09:06 AM
Hi Rugila

To state the obvious, a diagnostician diagnoses :D

In essence, I solve electrical & electronic problems in various commercial or industrial installations by gathering information about the effects that are causing concern, whatever they may be, and logically thinking through possible causes until I arrive at a hypothesis. I then seek to prove that hypothesis by carrying out monitoring and tests on the equipment or in its operating environment to confirm the presence of abnormal conditions or events, then recommend appropriate corrective/remedial measures for the equipment or the operating environment.

If that sounds a bit airy-fairy, it is because the scope and range of environments and conditions I work in is pretty much infinite and I never know where I will be next or what type of technology I will be working on. The only thing I know for sure is that there will be a problem, people will have tried to fix it and failed.

Every contract adds to my experience and knowledge, but in the end I rely on a very broad knowledge of electrical & electronic technology in general, good knowledge of a range of technological and manufacturing processes, general knowledge in a wide range of disciplines, and a perverse (peculiar?) mind-set that melds logic and lateral thinking into an effective diagnostic process. Of course I am aided by a raft of diagnostic instrumentation. Technology is an essential tool to complement the human side of the diagnostic process.

So, I'm not a medical diagnostician, but the processes are not a million miles removed in that I cannot normally open up the "patient" to look inside for clues so I rely on observational and listening skills to gather information then look for clues or symptoms that could produce the unwanted effects.

Not all problems are electrical or electronic of course, some are mechanical, chemical or environmental, and not a few turn out to be human but no matter, my job is to sort out what's going wrong and lead the client to an effective and hopefully economic solution.

Ergo, I am a diagnostician.

And it's the most fun you can have standing up! :8}

Cheers

Billy 8-{) :D

Heather P
05-02-2003, 09:19 AM
Billy,

I remember when I was a kid that Dad, a Mechanical Engineer, had an "air conditioning" problem at a rather large photo lab. Dust was settling on the negatives and causing all sorts of problems.

Turned out that although the lab was vacumned daily it was no-one's responsibility to empty the vacumn cleaner bag.

Can be interesting what Consultants are hired to find...

Billy T
05-02-2003, 12:06 PM
:D :D :D :D $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

rugila
06-02-2003, 09:09 AM
Hi Billy T.
Thanks for info about your diagnostic activities, you explained that very fully. Most interesting. I’ve done a fair bit of electrical work myself at different times and on various levels.
About 1915 Nicola Tesla used electricity to light a bulb on top of a rod in the ground some 30km away from the nearest power source. I tried that and it didn’t work, now I wonder why not … diagnostics division please help… It’s all fascinating stuff.
Regarding your applications of logic, you might like to work out the logical answer to the following question.

The local village had a barber who shaved every man in the village that did not shave himself. Did the barber shave himself or did he not?
(For avoidance of doubt regarding trick questions, the village women and children neither shaved nor were involved in shaving, and the barber neither went outside the village to get shaved nor called an outsider in).

Cheers, rugila

Big John
06-02-2003, 09:33 AM
> Now I can grab previously mentioned smartypants
> daughter when she gets home from school and show her
> something mathematical I know that she doesn't ]:)

Makes you wonder what they teach in schools these days. I think we got taught that sort of stuff in third form when I was at school. Certainly needed it for 5th form maths.

PS I easily did a uni course in maths but failed school c maths.
Reason. I was interested in uni whereas school c I was made to do it.

Billy T
06-02-2003, 09:52 AM
Interesting rugila, but that looks more like a paradox to me than an exercise in logic.

If treated solely as an exercise in logic, we can ignore the implied reference to the gender of the barber and the logical explanation is that the barber is a woman.

Another view is that the question contains an invalid recursive definition in that the barber appears twice, therefore it need not/cannot be answered.

My preferred answer is that since the question posed is paradoxical, I decline to accept that such a village can exist and therefore the paradox disappears, at leat it does from where I am sitting. :D

As I commented recently in another post, the electronic equivalent of this problem is that which we not so fondly referred to as a "chase me - ***k me" circuit, where logical diagnosis leads you round in perpetual circles.

Re Tesla's energy transfer exercise, I have read of this but never found sufficient information to form an opinion as to whether it was achieved or not. There seem to be several versions of the story and I guess one would have to find an authentic Tesla biography and history of his research and works to get any kind of hook on what may or may not have been achieved.

Cheers

Billy 8-{)

Heather P
06-02-2003, 10:35 AM
My best logical bets would be one of the following:

1. The Barber was a woman
2. The Barber was too young to shave
3. The Barber had a beard and didn't need to shave
4. The Barber has a skin condition which eliminates facial hair.

1 appears to have been eliminated so that leaves 2, 3 or 4

rugila
06-02-2003, 11:30 AM
Hi Billy T. Most interested in your response.
Several comments if you want to look at it a bit more.
(a) A paradox is an exercise in logic. Dispute that by all means if you wish, but before doing so you might like to look at e.g. W V O Quine's essay by “The Ways of Paradox”, where he discusses this and related questions in some detail. Look up his credentials and about his essay on Google if in any doubt. If you find Quine inadequate I can refer you to others.
(b) For clarification of avoidance of doubt, you can take it the barber is not a woman.
(c) Problems where a term occurs twice and thus do not need to be answered takes an interesting view of problems, but it’s not a view I personally would care to take.
(d) Your solution, which seems to be to assume the problem out of existence because you have difficulty with it, is a solution that has certainly been adopted by a lot of people, but not adopted by a lot of others. My own personal inclinations put me in the latter group. I think you may find there is a pretty heavy weight of philosophical firepower lined up against your view. Just where did you learn your logic?
(e) Your situation with Tesla seems somewhat similar. If you found the problem interesting, as I thought an electronic diagnostician might do, then maybe you might have been interested in getting a hook on what was achieved and how. Avoiding problems that cause difficulty is certainly a widely used way to not have to resolve them, but again ….
(f) Would you a good person to do my electronic diagnostics?
Cheers. :) :(

rugila
06-02-2003, 11:37 AM
Heather. For avoidance of any ambiguity, you can take it that:

1. The Barber was not a woman
2. The Barber was not too young to shave
3. The Barber didn't have a (non-fuzz)beard and did need to shave
4. The Barber didn't have a skin condition which eliminates facial hair.

If you'd like another version of the same thing that cuts out the distractions, consider which of the following comments is correct:

My comment immediately below is wrong.
My comment immediately above is right.

Billy T
06-02-2003, 01:07 PM
Sorry rugila, I took the question as being light hearted so my answers were a bit frivolous. To reply to your points:

(a) I don't disagree

(b) I did not seriously suggest the barber was a woman, that's just one option.

(c) is not dissimlar to (a)

(d) is simply one way of dealing with the question. It doesn't mean that at another time and place I might not choose to wrestle with it.

(e) ???? I have a deep and abiding interest in the works of Nicolai Tesla, I am simply saying I have not yet found any report of this experiment that is anything more than an unsubstantiated story. Since I don't claim to possess his genius, I will have to wait until I am enlightened by the discovery of more information.

I am reasonably well up on the theory of electromagnetic propagation and the physical laws that such energy obeys, and that quite possibly blinkers my view of other techniques Tesla may have employed. I tend to think in terms of the radiation of electromagnetic energy, and the means by which that energy can be detected and a proportion recovered at a distance. Lighting a bulb at 30kM is either very difficult or relatively straightforward, depending on how much energy is required to light the bulb and how much energy you have at your disposal to start with! Relatively lossless transmission of useful amounts of energy is another matter altogether.

Lacking the vision of a genius, I see the problem as one of effectively radiating sufficient electromagnetic energy to ensure that sufficient is available at the receiving end to light the bulb. Over 30 kM, even with highly directive and efficient radiating and receiving antenna systems, hundreds of kilowatts of energy are reduced to a few milliwatts at best. So you see, I can't see past the end of my nose on this one and must await enlightenment. It is a fascinating proposition and it is my view that if it is indeed true that Tesla accomplished this feat, one day perhaps we will see his papers or the technique rediscovered.

(f) Well, I guess you would have to ask my satisfied clients. I do not advertise and have more work than I can handle, all of which comes word of mouth. Whether you could afford to have me do your electronic diagnostics is another matter.:D

Cheers

Billy 8-{)

rugila
06-02-2003, 02:06 PM
Billy T.
I think it's all good lighthearted stuff and enjoy it. Doesn't mean that it should be light-thoughted though (not saying that your contribution is that).
Perhaps its good that you backed off from the logic debate since I'm sure this is arid stuff to most PressF1ers (although I find it most fascinating.)
So lets have another look at Nikola Tesla. (Your name for him, Nicolai, was one of Dostoevsky's Brothers Karamazov, so perhaps you've read that recently.)
Tesla didn't achieve his alleged feat through radiation of electromagnetic energy as you imply might have been his approach, I don't see that as feasible with existing technology. He used terrestrial stationary waves (through the ground) and achieved it by getting his resonances right.
I have an abiding interest in Tesla.
Billy, I'm sure you're a top electronic diagnostician and I'm even more sure that I couldn't afford you. Luckily no need to, since I can do all of my own stuff in that area very satisfactorily for my own purposes (inter alia I did a science degree majoring physics at Victoria University a while ago - and that's NOT a John Davy qualification.)
As to whether I could afford you or whether you could afford me, that also might be an interesting question.
Cheers, and happy diagnosing.
:) :) and more :)