×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Using formula without knowing it.
7

Using formula without knowing it.

Using formula without knowing it.

(OP)
Somebody has said that "if you can not derive a formula or if you can not understand how it is derived by others, never use it" do you agree with this?

RE: Using formula without knowing it.

I’d disagree.

Take for example Manning‘s Equation  for flow in pipes. It is an emphatical formula so you cannot derive it.

You don’t need to understand how he came up with that formula only that it works.

You do need to know the limitations and constraints on the formula and when and more importantly when not to use it, but you don’t have to be able to develop it from experimental evidence.

Rick Kitson MBA P.Eng

Construction Project Management
From conception to completion
www.kitsonengineering.com

RE: Using formula without knowing it.

I agree with Rick. Sometimes the necessity use a complicated formula greatly outweighs the need to understand it's derivation.

Reiterating Rick's 2nd point. It is VERY important, to understand when and where a formula applies. Otherwise, GIGO...


Wes C.

RE: Using formula without knowing it.

Emphatical = empirical?

Anyway, most formulae have a derivation or proof available either in a textbook or on the net. Someone who has a reasonable standard of maths should be able to follow most of them. Are there any in particular you can think of?

I use Laplace transforms now and then, and I'm damned if I can remember how they're derived. I've a book of standard transforms, and I've never considered proving them from first principles. These days I would probably experience a brain meltdown if I tried!

 

----------------------------------

One day my ship will come in.
But with my luck, I'll be at the airport!

RE: Using formula without knowing it.

The statement

Quote:

if you can not derive a formula or if you can not understand how it is derived by others, never use it

Is elitist BS foisted upon generation after generation of unsuspecting college students.  No one has ever found a closed-form solution to Navier-Stokes.  The Euler Equation made some extremely limiting assumptions (such as incompressible flow and zero friction) to solve part of it.  Bernoulli added some of his own fantasy's to Euler to come up with the famous "Bernoulli Equation".  Most people who can "derive" the Bernoulli Equation forget the assumptions that Euler and Bernoulli were very careful to explicitly state.  

Self-important berks who say "if you can't derive it, you shouldn't use it" do a significant disservice to their students.

Having completed that rant, it makes me very sad to see someone taking an empirical equation from a book and applying it without first asking "where does this apply?"  I talk to Oil & Gas engineers every day about multi-phase flow in a vertical conduit.  The most common correlation is called "Turner".  Mr. Turner did his research at elevated pressures and in his landmark paper said that it is not appropriate to extrapolate his work outside of the pressure/temperature ranges where he did his experiments.  Engineers feel like they're doing good work when they apply his equation 1,000 psi lower than his experiment.

I would restate the basic premise of this thread with:  "If you haven't verified that the assumptions and universe of an equation, don't use it."

David

RE: Using formula without knowing it.

As far as I'm concerned, as long as you can apply it, who cares how it's derived.

Mike

RE: Using formula without knowing it.

I would say anybody who is not familiar with the concepts behind Bernoulli's equation would quickly get lost in head losses due to friction. Laminar or turbulent flow (Reynold's number) or kinematic and absolute viscosity are concepts that a person using the formula must understand. The derivation of the horsepower in the pump/motor gains and losses is also something that must be understood. Tell someone that all the entities are in feet or meters and watch a puzzled look come over their face.

Someone using complex formulas must have an understanding of the subject.

RE: Using formula without knowing it.

Consider what happened in the Columbia tragedy. NASA knew that a large chunk of foam had come off and hit the wing at 400 mph, and they knew how roughly how large and how heavy the piece was. While the shuttle was in orbit, they decided to check and see whether the foam strike was likely to have done serious damage, so they got hold of an engineer at Lockheed and asked him to run some calculations, which were reportedly executed on an Excel spreadsheet. He used an empirical formula developed many years before by others, which he was apparently unfamiliar with, and which was intended to apply only to very small objects (such as micro-meteorites) hitting the foam. This gave a completely erroneous (and highly optimistic) answer, presumably because the mass of an object increases as the cube of the leading dimension, but the projected area increases as the square. Now I am not saying that it would have made any difference if this guy had found the correct answer, and it's easy to be wise after the event, but I think some would agree that it is food for thought.

RE: Using formula without knowing it.

A mathematical equation is nothing more that a model that gives approximate quantities to a situation between limits.  As an engineer you 'must' be able to 'reason' with the result and situation to which it is applied.  

I disagree with the view that you must be able to derive each equation in order to use it.  An understanding is enough and let reference books do their job when more is needed

The golden rule 'If in doubt ask'.

RE: Using formula without knowing it.

In some cases it can be better to remember where formulae come from rather than try to remember the formulae themselves.  Two examples from acoustics/DSP:

1) The relationship between frequency, wavelength and the speed of sound.  It's a simple relationship best derived each time you need it.

2) How to calculate the frequencies associated with data points following a DFT.

In both cases the formulae are trivial, but I often see people trying to look them up in books rather than understand them.

RE: Using formula without knowing it.

You really need to know the underlying assumptions and the intended applications of formulas, equations and even codes before you use them. Many times the assumptions are not clearly stated when the formulas are presented. Think about the TV commercial when the customer comes back with a car exhaust system that doesn't fit. The parts counter states "Book says it fits". Exactly what we don't want to do as engineers.

RE: Using formula without knowing it.

I don't think you have to know what the formula is or how to derive it, but you do have to know when it is applicable, and what assumptions are included in teh use of that formula:  English Muffin's example above shows what happens when you just plug numbers into a formula without knowing it's limits.

The best ocurse I ever did on multiphase flow in pipes was one given by a software manufacturer on their vertical lift programme for the oil & gas industry.  The software came with a whole host of different correlations& the guy gave a sheet isting the applicability of each correlation: 'limited to small diameter pipes', 'limited to GOR below 500', and so on.  So now I know to use the Fancher & Brown correlation as this usually gives the lowest pressure loss, and Duns & Ross as this usually gives the highest pressure loss as a check on the data, and then to start actually loking a the results instead of picking the first correlation on the drop down list and designing off those results....

RE: Using formula without knowing it.

2
Elitist argument like this is what forces unnecessary, obsolete analytical mathematics on generations of new engineers while important, useful subjects go untaught for lack of available course time!  We spend so many lectures getting people to the state of the art of mathematics in the early 18th century, and then we sell this as a rite of passage to new engineers and a means to teach them to "think".  Hogwash!

Clearly, an engineer has a responsibility when using someone else's work (whether that be equations, correlations, experimental data, drawings, specifications etc. etc. is irrelevant) to make themselves aware of the limits of applicability of the work in question.  Being able to derive the equations yourself is going above and beyond the call of duty in most cases.

RE: Using formula without knowing it.

Pythagorus is credited with the proof that the square on the hypotenuse is the some of the squares on the other two sides.
He provided the proof but the relationship was known and used for centuries before that.

I doubt if every user was able to derive the relationship and until Pythagporus, no one could prove it which, importantly, presumably meant that no one could say for sure if there were situations when it didn't apply.

Perhaps we should recognise that deriving somthing is very much more difficult than re-creating it and perhaps this would be a better way to consider some equations. That is, you don't need to have the same creative genius to develop the equation in the first place but might, perhaps, be expected to be familiar enough with recreating the equation or its shape, without all the proofs that go with it. I should also hope to have sufficient familiarity with any equation I use regularly to develop a "feel" for the conditions where it can be used and the results I would expect. One trick taught to me was to do approximations to develop that feel i.e. to use easily calculated order of magnitude values to arrive at a "ball-park-figure" then do the actual calculation and make sure the result obtained was within the expected range of values.

JMW
www.ViscoAnalyser.com

RE: Using formula without knowing it.

Perfect example.

How many here have ever used the Pythagorus’s Theorem and how many can derive/prove it?

I have and I can’t.

Rick Kitson MBA P.Eng

Construction Project Management
From conception to completion
www.kitsonengineering.com

RE: Using formula without knowing it.

I've heard similar and I'm sure the person had good intentions.

Isn't the saying similar to "If you can't design a structural member size by hand, do not use a computer program."  For this instance, I would agree with the statement.

It is also similar to "If you can't calculate by hand, do not use a calculator."  I would partially disagree.  I wouldn't dare hand calculate a square root of any number to the hundredths.

I agree strongly with wes616 about GIGO.  It is important to understand where and how a particular formula should be applied.

Time is more of the essense than it was in the past.  Computers definitely can reduce the design time.  It would be wrong as engineers to rely on input-output without fully realizing the capabilities and limitations of any software.

I believe the person who said the above statement had good intentions and wouldn't take it too literally...

RE: Using formula without knowing it.

The theorem of Pythagoras is only correct for plane geometry. The postulates which are needed to prove it are not correct for other types of geometry, such as spherical geometry. A surveyor who assumes that the world is flat will discover that his measurments don't add up over long distances.

It *is* necessary for engineers to understand enough about any mathematical theory to know the conditions which are necessary for that theory to be valid. Both space shuttle catastrophes were caused in part by engineers who blindly applied formulas or software without understanding the limitations of the models they represented.

RE: Using formula without knowing it.

Although slightly off topic, here is another classic example of a disaster caused by engineers blindly applying and relying upon "state of the art computer analysis" which they do not seem to have fully understood.
http://www.eng.uab.edu/cee/reu_nsf99/hartford.htm#asce
These guys apparently did not realize (or ignored) the fact that the analysis package did not consider buckling.
Of course it could, and maybe will, happen to any of us - but usually it doesn't have this sort of consequence.

RE: Using formula without knowing it.

Coo. My final year project was (partly) on torsional instability of truss members!

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Using formula without knowing it.

OK so... you can use a formula...

if you can derive it AND are sure that the formula you apply is applicable under the given conditions,

OR if you can validate the answer with a sufficiently accurate/reliable hand calc.

RE: Using formula without knowing it.

no wait...

validate AND (derive OR applicable)

I think that should be it

RE: Using formula without knowing it.

No, we don't need to know how to actually derive a formula in order to use it, but to use it intelligently we do need to have an understanding of where it came from and what limitations should be observed in applying it. When you calculate a result using the formula, you should be able to look at the result and make a decision about whether or not the answer is reasonable and makes sense. Many young engineers that I have taught seem to lack the ability to question the result that they calculate with a given formula, even if it is off by several orders of magnitude. Did they enter each quantity in the formula with the proper units? Did they make a mathematical error in the calculation? Are the units that they are using compatible the units assumed in the derivation of the formula? By failing to consider these potential mistakes it reveals a deeper problem - that they lack insight in the problem that they are attempting to model.

Rick, consider a right triangle with the sides that border the 90 degree angle labeled A and B, and the hypotenuse labeled C. Then, if the angle between the hypotenuse and side B is Theta, we can write

sin(Theta) = A/C

and

cos(Theta) = B/C

You can use these relationships to derive the Pythagorian Theorem. Using the trigonometric identity

[sin(Theata)]^2 + [cos(Theata)]^2 = 1

we find

(A/C)^2 + (B/C)^2 = 1

Multiplying both sides by C^2 we find

A^2 + B^2 = C^2

This is the Pythagorian Theorem. For an actual derivation, look at the content in the following link:

http://www.perseus.tufts.edu/GreekScience/Students/Tim/Pythag'sTheorem.html

RE: Using formula without knowing it.

Is that not circular logic being used as a proof?

Does not the SIN^2 +COS^ =1 come from the Pythagorian theorem?

In other words are you using an equation derived from a theory to prove the theory?


Rick Kitson MBA P.Eng

Construction Project Management
From conception to completion
www.kitsonengineering.com

RE: Using formula without knowing it.

Rick, it wasn't intended as a proof. It was meant to show how the relationship could be arrived at from a simple trigonometric principle and some geomtrical arguments. Yes, you can easily show that the reverse works as well - the trig relationship can be derived from the Pythagorean Theorem. The actual proofs, based on first principles, are contained in the links listed below:

http://www.jimloy.com/geometry/pythagz.htm

http://mathforum.org/isaac/problems/pythagthm.html

Hopefully these links will work (as opposed to the one I listed in the previous post).


Maui

RE: Using formula without knowing it.

Maui,
now you have to show/derive your trig relationship.... (pretty soon we'll be back onto Russel).. so at what point do you stop re-creating the entire history of maths, science and engineering?
Everything depends on something else.

JMW
www.ViscoAnalyser.com

RE: Using formula without knowing it.

maui, that's pretty complicated...
Try this: draw the triangle with lengths a, b and c (a and b form the 90 deg angle). draw the square with sides c and draw 3 other same size triangles on the other sides of the square. The area of the square = c^2 and it equals the area of the 4 triangles plus the smaller square, or 2*a*b + b^2. Solve for c^2: c^2 = a^2 + b^2.

RE: Using formula without knowing it.

Problem with that approach is that it is only feasible for integer sides.

I must admit I burst out laughing when Rick first mentioned it, it is such a neat example of a useful formula we use every day, yet I'm betting that only one in a thousand of us could derive it without looking it up first (cue 400 proofs of Pythagoras). I've never even read the full proof.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Using formula without knowing it.

"epoisses approach" should work for any length sides. And what is an "integer side" exactly ? Wouldn't that depend on an arbitrary choice of unit ? As far as I know, the only objection to that solution is that it employs algebra, unlike the classic solution given by Euclid.

RE: Using formula without knowing it.

It works for any length sides, I learnt it at high school from a maths teacher in his last year before retirement, who was no less than God to me at the time at least when it came to maths. So don't break my heart and burn down his proof please!

RE: Using formula without knowing it.

Well, at this point, it's clear to me, that none of you should ever use the Pythagorean Theorem again.

Good Luck
--------------
As a circle of light increases so does the circumference of darkness around it. - Albert Einstein

RE: Using formula without knowing it.

epoisses proof is shown on maui's link,
and as englishmuffin says it is not restricted to integers.  i think the "integer" thought comes from it is easy to make a 90degree corner if you can make a 3unit length, a 4unit, and a 5 unit.

RE: Using formula without knowing it.

Actually, there is an even more elegant "proof" - requiring the addition of only one construction line - which can be found, among other places, in Roger Penrose's new book "The Road to Reality" (about the current state of the art of knowledge in physics and mathematics. Excellent book by the way.

RE: Using formula without knowing it.

I guess what you mean is draw a line from the 90 deg corner that lands at a 90 deg angle on the hypothenusa, then express the area of the large triangle as the sum of the areas of the smaller two expressed as ratios:
1/2*a*b = 1/2*a*b*b^2/c^2 + 1/2*a*b*a^2/c^2

This does not sound like a current state of art / cutting edge recent mathematical invention, if a dumb @$$ like me can repeat it after a simple hint?

RE: Using formula without knowing it.

PS ok I saw my proof back in one of the links, it appears that some Babelonian did it already long before Pythagore, that reassures me.

Something else: when I had worked for about 2 months as a chem eng, one of the operators asked for a simple formula to calculate the content of a horizontal drum as a function of the level height. I was glad to be able to use some math again and gave him an excel sheet with a few sines and cosines. My fellow engineers feel off their chairs with surprise. Then I wrote down an integral and worked it out to find another formula that did essentially the same but was more impressive. They fell off their chairs once again and stayed on the floor for about half an hour with astonishement.

Half a year later I found that formula back and was unable to tell how on earth I had done it. Right now (9 years later) I don't even try to imagine where my university calculus has gone, I wonder if I might be able to pick it up again.

Is yours as rusty?

RE: Using formula without knowing it.

I started graduate school 12 years after finishing under graguate.  My most common comment was "I can remember having known that".  It came back reasonably quickly.

David

David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

RE: Using formula without knowing it.

actually englishmuffin, that proof is on the earlier link too, and is attributed as an ancient historical proof

RE: Using formula without knowing it.

can we leave pythagoras and agree that there are many ways to "skin a cat" (the trouble, of course, is finding one that will sit still long enough)?

can we return to the OP ?  I personally think it is nice to be able to derive the equations i use.  i think being able to allows me to understand the equations (and the assumptions) better.  like the previous poster, david, there are many things i'm sure i use in daily practice that i've forgotten the derivation (lets take the parallel axis theorem, why does one axis have to be thru a CG ?) but i'm sure i could sit down with a book and understand the details (again).  i don't think it's elitist to be able to do this, possibly others have an inferiority complex if they can't ??

RE: Using formula without knowing it.

A very interesting thread - Pythagarean's Theorum notwithstanding.  I am a geotecthnical engineer.  Did I ever go through the graphical and proof analysis of Bishop for slope stability by slices; yes, I remember seeing it done. Could I do it now.  No. Would I want to - No.  But I do know that it is well established.  Similarly with bearing capacity computations.  I understand well the overall development but the intricacies of the Nq and Ng and Nc derivations and differences between those of Terzaghi, Meyerhoff, Hansen are, well, outside my current need (desire?) to know.  Again, it has been well established as to which is the most reasonable.  Same for Nq values in pile design.
   Now, on the application.  As I said in other forums, I am not against computer programmes.  I undestand that for many other disciplines, they are an absolute necessity.  For my discipline, well, I can live without them (if I don't care about the time element).  I do most of my calcs as back of the envelope and develop further if needed.  I do most calcs, anyway, by hand for it is quicker than hunting for a computer programme that I don't have.  Too many spend more time finding "a" programme for which they have no idea of the limitations and accuracies of such.  For those with a good background in hand methods, they can be reasonably sure of preventing GIGO complications; but for those who are new to an analysis or may be stepping beyond their field and experience, it can be fraught with danger.  
  In the end - if you use time-honoured established methods, understand the assumptions and caveats on a particular method; have a experience to know that that your answer is not garbage, then it isn't necessary that you can derive your equation from first principals - each and every time!
 

RE: Using formula without knowing it.

Sorry, what I meant by integer sides is that you have to be able to prove that the area is always the square of the length of the side, which can only be done physically if you can fit (say) 25 unit squares into a 5x5 square. Otherwise you are assuming the analytical solution.

So can anybody prove that the area of a square is always L^2?

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Using formula without knowing it.

Greg Locock : I am going to get hammered if I keep replying to these off topic things, which I always find more interesting than the original questions. I think I see what you are getting at. It presumably all comes down to the problem the Pythagoreans had with irrational numbers. I don't see an issue with the area of a specific square associated with a line of length L1 being L1^2. I think the problem comes when you define another line of irrational length relative to the first, and try to prove that the relative areas associated with the two lines are in the ratio L1^2/L2^2. I think all this has been rigorously figured out by mathematicians, but as I (sort of) suggested before, you do have to be careful about mixing geometry and algebra if you want a rigorous Euclidean style proof.

RE: Using formula without knowing it.

(OP)
My intention is you must thoroughly understand what the formula is about and if you are given the proof of the theorem you should understand it.

RE: Using formula without knowing it.

19652022,

Back to your original question and responses from many, what do you feel the answer is?

RE: Using formula without knowing it.

Surely we must recognise a difference between mathematical theorems like the cosine rule, trig identities, roots of a quadratic equation etc. which can be derived logially from basic axioms and engineering formulae which are approximate mathematical models of physical systems. In the latter case it is essential to know what assumptions were made in the derivation of the formula even if you don't actually know how to derive it.

If I wanted to know how much tip force is required to deflect a cantilever box beam (length 1m and cross section 0.2 x 0.2 m made of 2mm thick steel) by 0.1 m, I could plug the numbers into a formula derived from Euler beam theory and get an answer. It would be a very wrong answer however (because of assumptions about small displacements, linearity of stress-strain relationships - Hooke's law, Neglecting 2nd order terms in strain-displacement relationships - Love's elasticity postulates, omission of shear deformation effects  etc. etc.).

OK, this is an extreme example, but I can think of plenty of others.

M

--
Dr Michael F Platten

RE: Using formula without knowing it.

speaking of off-topic, 19652022,  is your handle a partial phone number or did your cat walk across your keyboard as you typed in your profile?  I've been wondering ever since your original post.

ps, as someone who recently went back to school, and had to re-learn formulas and concepts, I find I enjoy learning where something comes from and how a formula was derived.  I'm no longer satisfied to learn just enough to get the grade I need if it means compromising a real understanding.

"If you are going to walk on thin ice, you might as well dance!"

RE: Using formula without knowing it.

casseopeia,

"if you are going to walk on thin ice, thread lightly and carry a balloon"

RE: Using formula without knowing it.

If you really want to understand something, teach it to others.

LewTam Inc.
Petrophysicist, Head Stockman, Gun Welder, Gun Shearer, Ski Instructor, Drama Coach.

RE: Using formula without knowing it.

I, like Cass, am going to school to get the ABET degree.  I have worked in the engineering, surveying field for 30+ years and have worked both inside (designing) and out (making the design work).  The problem to me with school is with the example, problems, etc. being so otherworldly with their intended content.  It has actually hurt me that I have the real world experience.  I will work the problem and the answer will be ‘the flywheel turns 90 billion RPM.’  I know in my heart that this cannot be right, so I will try reworking the problem and again….  The problems that bug me are working out everything on the computer when the back of an envelope will do (knowing how to work the numbers correctly but not knowing what they mean) and not knowing what the builder need from the design people.  Example – designing the CL of a manhole down to a eighth of an inch not knowing that they are normally put in to the nearest 6 inches or so.  

John

RE: Using formula without knowing it.

[quote]If you really want to understand something, teach it to others.[unquote]

Those who can, do.
Those who can't, teach.
Those who can't teach, administrate!

----------------------------------

One day my ship will come in.
But with my luck, I'll be at the airport!

RE: Using formula without knowing it.

Those who can, do.
Those who can't, teach.
Those who can't teach, lecture

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

RE: Using formula without knowing it.

There seems to be a lot of egos floating around in this thread ... "Why do I need to know where it came from to be able to use it?"

Fair question ...

Of course you can use equations / formulae without knowing where they come from, or how they are derived ... but only a poor engineer would do so.

For example, I look up a text book, it says that the average velocity of a fluid flowing in a pipe Vave=0.5* Vmax.

That formula is true.

But if you didn't know where it came from, you wouldn't know that it is only applicable for laminar flow.

It is IMHO VERY important for students to learn the fundamentals. From the fundamentals you can derive what you need. They give you a better physical understanding of what is actually happening, in this case momentum transfer between the walls of the pipe and the fluid, and viscous transport of momentum within the fluid.

In my mind, universities / teaching institutions teach people how to teach themselves - they are not in the buisniness of mass producing people who will enter the workforce and immediately able to do the same job as someone there for 20 years. Therefore AFAIC, universities SHOULD teach the fundamentals, and engineers SHOULD make it their buisiness to know, at least in general, where the equation came from.

Comments like "Those who can't, teach." are very tiresome and juvinille. They imply a certain amount of arrogant snobery ... get off your high horse.

By the way, I'm a process engineer, not a teacher.

Read the Eng-Tips Site Policies at FAQ731-376  

RE: Using formula without knowing it.

Quote:

Those who can't, teach

I'd say that those who can't, make bad teachers.

RE: Using formula without knowing it.

I'm married to a teacher: I'm allowed to say it!

In honesty I couldn't do her job any more than I could fly. I've got neither the patience nor the self control to get through a day trying to educate disinterested kids. I'd end being arrested before the first day finished. Good teachers are worth their weight in gold. Bad teachers can kill a kid's interest in a subject so easily.

There is an element of truth in the "Those who can't, teach" comment because teaching pays less than industry, and the most able will be attracted to the higher paid positions. Those that are left are either the also-rans or those who just really want to teach. My wife is the latter - devoted to her job.

----------------------------------

One day my ship will come in.
But with my luck, I'll be at the airport!

RE: Using formula without knowing it.

I always thought that those who can't become consultants..?

RE: Using formula without knowing it.

ScottyUK,

My spouse is not a teacher but I know of many colleagues' wives that are.  I was led to believe in the past that teachers (K-12) make low salaries.  However, when considering their salary at an hourly rate, it is not bad at all (Factor in three months summer vacation, one month winter vacation, a week of spring break and most national holidays).

Many engineering professors have double income being a teacher and consulting in their field outside the university.  Not a bad deal.

For an engineering career, the job gets progressively more challenging as one becomes more experienced, teaching career appears to get easier.

RE: Using formula without knowing it.


I think some of the crisp sayings attributed to Einstein are appropriate at this stage:

Quote:

As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.

Quote:

Education is what remains after one has forgotten everything he learned in school.

Quote:

We can't solve problems by using the same kind of thinking we used when we created them.

Quote:

God does not care about our mathematical difficulties. He integrates empirically.

RE: Using formula without knowing it.

(OP)
Casseiopapea,
This is just my Id i prefer.
Whiyun,
I think you should understand the formula you are using whether you can derive it yourself or somebody has derived it.
Thaanks a lot for all participants. Thanks a lot for ENG-TIPS Forum for such a live and interesting discussion.

RE: Using formula without knowing it.

Einstein said

We can't solve problems by using the same kind of thinking we used when we created them.

Excellent

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources