teachers, and the magic called ‘vernier’ callipers


This happened some 10 years back or so, and I have reproduced the journal/notes below (with a few additions) –  just to help you reconfirm your valid opinion that, I am a weirdo. Thanks.


…For the past few sessions, we (erdkinder (this is montessoriese for an adolescent) and I) have been studying/learning about measurements, precision, accuracy, error, terror ad infinitum. As part of this and with a view to addressing the ‘syllabus’ requirements of the eminently (in)evitable 10th stuntard exams, the children have to study about Vernier Callipers, Screw Gauges etc.


Now, I have always been fascinated by this ingenious concept of Pierre Vernier, but I recall that, when I ‘studied’ his wonderful ideas a few decades back, it was quite sad; my illustrious (then) teacher (RIP) ‘covered it’ without a clue, though the concept is fascinatingly simple.

Same story got repeated during my baccalaureate studies too. Unfortunately, I realized it only later that all these folks merely taught because they were paid to teach, and NOT because, they loved to teach nor were they men/women who were fascinated by the world of  ideas.

May be the reason is that teaching is such an underpaid job, in spite of it being exhausting and sometimes saddeningly thankless, and hence is mostly dominated by folks, who are/were otherwise ‘rejects’ from the ‘system’ – meaning, highly paid cushy jobs; or, it may be that it is a sadly negative feedback system in which good folks can’t get in for various reasons – and the folks who are there in the system, have lost all enthusiasm for life and so curiosity is dead in them.

Of course there are exceptions, but then I believe, exceptions only prove the general rule. This is not to say that I did not have good teachers and I have thusly a bunch of axes to grind – I have had my own delightful quota of exceptions but they were mostly outside of the walled gardens of acadummya. heh!

But, by and large, there is so much joy in teaching, learning and being with children (ah, the luxury!) that, if by some magical poincare inversion, if teaching becomes the highly paid and most respected profession – then… the result would be a deliriously delightful future, what else, but may be am merely dreaming or better still, smoking marijuana!

Now for a commercial break! 🙂

Luckily, all teachers (‘adults’ in montessoriese) in our school are there because they either love the children or love the montessori education mode – and mostly & actually it is both. It is a  real pleasure working (and getting workedup) with them. Thank dog for small mercenaries, am not talking about the cutely brattish young fellers and fellerinas at the primary environment (this is ‘class room’ in montessoiese), though..

Getting back to the rant…


Considering, how important this teachers’ role is in/for the society, it is amazing, but is true in general all over the world, that the status quo of the vicious  cycles of terrible mediocrity continues – such as:

–>>  bad teachers -> bad students -> worse teachers -> abominable students -> ayyo teachers -> NEET protesting dumbass students, especially from my dear TamilNadu-> COMPLETELY USELESS teachers -> more FANTASTIC idiots, but with 100% marks ->> >> >>>… … …

…Of course, there has been one significant exception – ‘Soviet’ Russia – which alas or happily so, is no more.

Is the concept ‘water finds its level’ applicable and operative here? Would this theory help one understand this breed of abominable know men and women? Would this be the result of parents happily outsourcing the ‘education’ to the schools, as they think that, with transfer of genes (le vice?)  their contribution towards their children is over – except in the case of  buying the new, latest and improved Tablets? For all I know, my neighbour’s golden retriever only knows…


Ayyo! Pierre Vernier beckons.  He has been waiting patiently for my rant to end, and I respect him for that too!

OK. The idea of any measurement is to allow to us to have a reasonable take on something to be measured – and that which is possible with predictable accuracy and precision. In a given scale (Ruler, that is – not very despotic, I hope) graduated in centi and millimeters, the minimum measurement (technical jargon: least count) that is possible would be 1 mm; this is also normally called ‘pitch‘ – but I intend queering it.

Now, <drumroll> here enters the French man (actually he did this nearly 4oo years back! BRILLIANT!) who decided to use a scale (vernier scale) that had ten divisions that were equal to 9 normal scale (‘main scale’) divisions. Hence each vernier division had a least measurement possibility of 0.9 mm.

Now comes the magic. If these two are brought together / juxtaposed then it is possible to measure lengths accurate to 0.1 mm. The least count of the combination of scales is 0.1 mm! How?


At our funda school, we worked with mere paper strips. I gave the children 2 strips each (some 1 cm x 10 cm – the size does not matter, dinosaurs notwithstanding – but we will call them A and An just to confuse you). One of the strips A was folded into 10 equal parts and marked off appropriately – the other strip An was placed over the first and was reduced/cut-off to measure 9/10ths of A. In other words Lengths of (A/An) = 10/9. An is also folded into 10 equal lengths and is marked off. All reasonably approximate of course.

A = mein skale. An = vernier scale.

Now, if you juxtapose them in such a way  that the markings face each other, Voila – at any point any ONE division mark of An will coincide/align with some division or the other of A – if you move A and An against each other! Yay! There is a picture of it below to befuddle you more!

how to understand 'vernier' using paper strips - you can move them against each other,,, (the newspaper just serves as a background)

how to understand ‘vernier’ using paper strips – you can move them against each other,,, (the newspaper just serves as a background)

From this, it is a small baby step ahead, to understand how the magic works, nothing earthshaking, but beautiful! Of course, the children understood the cutting edge technology with a little bit of steering etc. I am proud of them.

If you are curious about how this concept works or if your engineer neighbore wants to know it, just go ahead and hustle any of our erdkinder. They will be happy to enlighten…

Erdkinder macht frei. Ja.

:-) Would any of you want to share your idea as to how this damn vernier works?


roughcut ideas, opinions & notes on education


8 Responses to “teachers, and the magic called ‘vernier’ callipers”

  1. RC Says:

    அருமை அய்யா,
    நன்றிகள் பல.
    சிரித்து மாளவில்லை சில வரிகளைப்படித்து எனக்கு.

    என்னுடைய படிக்கும் பழக்கமானது பொதுவாக வரிகளைத் தாவித்தாவி நோக்குவதும் சரசரவென்று நடுவில் உள்ள வார்த்தைகளை ஒருவகையாய் யூகித்து ஓடும் வகையிலானது.புரியவில்லை என்று தோன்றினால் மட்டுமே மறுவாசிப்பு உடனே செய்வேன்.[ஒரே பதிவை மறுபடியும் படிப்பேன் சிறிது நாளோ/மாதமோ தள்ளி ஞாபகத்தையும் புரிதலையும் உறுதி செய்ய..அது தனி ]
    இன்றும் அவ்வவகையில் ஓடும் பொழுது, ‘Thank God’ ஆக பொருள் குழம்பி வண்டி மக்கராகி நின்று விட்டது கடைசியில் ‘Thank dog’ கவனிக்க ‘God’ தான் உதவி செய்தார் :-)
    திராவிட மரபணுவில் உள்ளது ஆங்கிலேய பரமணுவா? [le vice?]  :-)
    தொடக்கப்பிழைகள்[!] விவரணை போதும் என்று நினைக்கிறேன்


    சதா ஓடுவதில் தவறவிடுவது – ‘துல்லியத்தையும்’ ‘சரிநுட்பத்தையும்’ [Precision,Accurate முழி பெயர்ப்பு சரியா?]
    மாறாத அளவுகோல் மேல்[உடன்?] மாறும் அளவுகோல் உட்கார்ந்தது தானே வெர்னியர் அளவி .இரண்டும் இணைவது நுட்பத்தை உணர்த்த [ஸ்ருதியும் ஸ்ம்ருதியும் போல].

    அளவீடுகளும் தராசுகளும் அளவியலை[metrology] மட்டுமே உணர்த்துவதில்லை சித்தாந்தங்களையும் கூட

    புரிதல் தவறெனில் உணர்த்துங்கள்.

    நன்றிகள் வாத்தியாரே மறுபடியும்.

  2. Jayaram Says:

    Please add a statutory warning as well… “This blog can be infectious while driving”.. I was moving the “A” and “An” scales up and down as i was driving down to office

  3. From Jayram:


    Now we know in the “An” vernier paper scale every main division is equal to 9/10 of cm which is 9 mm.. Now i will further mark 10 equal divisions within each division of vernier which makes each small/minor division in vernier as 9/10 of mm= 0.9.mm.

    Now to measure length of an object,,
    1) will make a folding in the “A” main scale where the obect ends..
    2) Will take the “An” vernier scale to start at the nearest left main division of the main scale (Let us assume this to be 3 cm or 30 mm)
    3) Now the folding will match with some minor marking in the vernier scale,, For example if the marking happens to be at 5th minor division of the vernier then the measurment would ne 5*.9= 4.5mm or if it happens to be at the 6th minor division then the measurment would be 6*.9=5.4mm and so on… Now i will add this to the closest left main division we had taken in step 2 which was 30 mm..
    4) So the overall length would be 30 + 4.5 = 34.5 or 30+5.4= 35.4 mm..

    • MaheshC. Says:

      A has 10 divisions of let’s say X. So 1 division of A is x/10.

      An has 10 divisions too, but of 9X/10. So 1 division of An is (9x/10)/10 = 9x/100.

      When you slide An over A so that their first markings are juxtaposed, the other markings get arranged near to each other such as to effect the following operation:
      1 division of A minus 1 division of An = = x/10 – 9x/100 = x/100.

      If x is 1 cm, then the other markings of these two scales get arranged such that any two A and An markings nearest to each other will be at a distance of 1 cm/100 = 10 mm/100 = .1 mm.

      Correcta saar.?

      P.S.: Idha school leya naan padichirukalaam aanaa padikalai.!

  4. Anonymous Says:

    Thanks a lot for explaining the interesting concept of Pierre Vernier. I request you to write more articles regarding education at primary level. Please share some reference in this regard.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: