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The Commando Method

Wednesday, November 12, 2008

One of my most favourite academic possessions in middle school used to be my geometry set.

I still remember that light blue, shiny plastic case, with “Dux” printed inside a dark blue circle on its lid. In those days, anything from Dux used to be a status symbol, whether it was a simple eraser or an “ink remover”; even Staedtler couldn’t attract as much envy as Dux. Dux just used to declare out loud that the students carrying its products take the straightness of their lines and the roundness of their circles seriously.

Not to mention that compasses, and specially dividers, from Dux could also be utilized as accurate weapons. Accuracy was everything when you wanted to plant a compass under the seat of your “enemy” — quick and lethal, but also subtle. Sleight of hand, of course, was also important, so that you could swiftly recollect your compass, taking advantage of the ensuing chaos in the classroom after your enemy would jump two feet into the air and start rubbing his butt while yelling like a yeti.

But anyway, this post is not about such misadventures. It’s about a certain method that we discovered while doing geometry exercises.

I don’t know about others, but I actually used to enjoy drawing all those triangles and circles using just a sharp pencil, a compass, and a ruler. Somehow, it just felt magical to align the ruler, draw some lines, use the compass to draw arcs and circles, and then see some geometric figure appear on the paper. It was like constructing a small house, brick by brick. The sense of accomplishment used to be overwhelming at times.

Take the following figure, for example…

Incircle of a triangle

It’s an inscribed circle, or incircle, of a given triangle. (Everything drawn with the help of a ruler is red; green elements use the compass.) Now an incircle is a circle which is inside a triangle and touches all of its sides. Simple enough. You start by drawing the triangle according to the specification given in the exercise in your textbook. Next, you bisect all the angles of that triangle and find the point where the bisectors meet. You then take that point as the center of the incircle, and adjust the angle of the hinge of your compass so that the radius of the circle you are about to draw equals the distance between that point and any of the triangle’s sides. Finally, you draw the circle. Clean. Perfect. Magical.

Unless — yes, there is an unless — something goes wrong, which used to happen quite frequently.

Most of the time, it used to be the compass. Your enemy’s butt would sometimes damage its accuracy by making its hinge go loose, or by disturbing the alignment of its pin. A price that you just had to pay.

So instead of that perfect figure above, you could end up having something like below. (Notice that the incircle is not touching the side BC.)

An incircle gone wrong

At this point, me and my mates used to have two options. One, erase the unsuccessful drawing and start again. From scratch. This used to take a lot of our time. To add to our misery, Murphy’s law also used to spring in action, making matters worse and keeping us frustrated.

Second option was to cheat. But we didn’t like the word “cheat”, so we rephrased it. We started calling it “the commando method”.

Here’s what you do in the commando method. You erase the side BC carefully. Again, the eraser from Dux used to come handy with its sharp edges. (Staedtler erasers also used to work fine in this case.) You then redraw it, and make sure that it touches the incircle.

An incircle after the commando method

Clean. Perfect. Magical.

Of course, the commando method demands some changes in rest of the figure as well. For example, a slight change in angle B, decrease in length of the side AC, and adjustment of the bisector for angle C.

But thankfully, our math teacher used to be a human and not a robot. She could spot the difference between an angle of 45 degrees and an angle of 40 degrees, but not between angles of 45 and 46 (or 45 and 44) degrees. Similarly, addition or subtraction of some millimeters in the sides of the triangle would also escape her usually hawk-like eyes.

This, however, is the simplest case for the application of the commando method. Consider, for example, the figure below. It needs a certain level of experience with the commando method in order to get this figure right.

An incircle gone wrong II

And finally, the commando method would completely fail if you end up with something like the following figure on a lined notebook.

An incircle gone wrong III

Why, you ask? Because the base of the triangle was always drawn by us on a line in our math notebooks. Re-adjusting the base would move it away from the line, and that literally screamed “CHEAT!” at our math teacher. If, however, a blank page is being used, then the commando method can be applied without any hiccups. (But if someone is competent enough to draw the base of a triangle without any help from a line already present on the page, then s/he shouldn’t probably be needing the commando method anyway.)

With the passage of time, we learnt to apply this method for other exercises in geometry as well. Later on, we extended it to forge proofs of our work in the physics lab. Optics experiments, in particular, provided a magnificent playground for the commando method. In optics, some experiments included erecting a couple of pins on a sheet of paper, then looking at the images of those pins through a glass slab or a prism, and then aligning those images with another set of pins, which actually meant that we were tracing the path of the light rays through that glass slab or that prism. Commando method used to save us all the touble: we would start with drawing the resulting figure by copying it from our textbooks (with all the correct angles and all), and then poke pins on its lines, successfully indicating that the figure was drawn after the images of pins were aligned, when in fact, we hadn’t aligned any pins at all.

And believe me or not, we actually learnt a great deal while applying the commando method. Concepts of optics, such as refractive index and critical angle and other things from the same tribe, made much more sense to us after we cheated on their experiments. Honestly. We knew exactly what to do during our physics practical exam in matric, and nobody among us scored below 20 (from 25). Nobody applied the commando method either.

Now it’s been so long that I have used the commando method, that I miss it.

And I miss Dux as well. Some months before matric, there was a swarm of fake Duxes in the market, and the real Dux also disappeared somewhere, with the quality of its products declining. I have no idea who the current market leader is for geometry sets these days. And come to think of it, I don’t have an idea about anything these days.

If only I could apply the commando method to understand not just optics, but other things as well.


circle, compass, geometry, geometry set, optics, ruler, triangle

(Possibly) similar posts


Ordinary Girl

Nov 12, 2008 at 11:21 pm

Awww…Saadat, good old days! I also LOVED doing geometry exercises in our Maths class. It was,as you said, magical. Ofcourse, sometimes had to resort to commando actions like you mentioned but it was an amazing feeling when I used to get it perfect the first time. :)

Kia yaad karwa dia, bhai…geometry, uufff…mera piyara red color kaa Dux ka compass! I still have it! And it’s as accurate as ever. :)


Nov 13, 2008 at 11:13 am

I loathe math.


Nov 13, 2008 at 11:56 am

lol @ commando method
and yea thank god our teachers were humans and not robots….otherwise pata nai kitni baar fail hoti main :P

Dinky Mind

Nov 13, 2008 at 2:46 pm

Lol…Very nice post :D I wish you had posted your Commando Method when I was in sixth grade :( But I’d surely teach this thing to my younger bro :D


Nov 13, 2008 at 7:03 pm

i read the first line and the last line, this post is certainly the new commando method to put someone to sleep, it even beats the ‘sleeper hole’! :P

Hira S.

Nov 13, 2008 at 9:24 pm

oooh! I did that a lot too! especially in physics. I used to memorise the answers to the mcqs from past papers because i knew my teachers werent smart enough to come up with anything on their own , thus even though i understood zilch i still got A’s!
and during first year practicals i had the pendulum, so i didn’t even bother doing the practical. just swung it to n fro n wrote down the readings i knew i’d get anyway.


Nov 13, 2008 at 10:09 pm

I hate, absolutely despise Math. :S


Nov 14, 2008 at 5:55 am

Do I look green? Because i feel… *tries to stop looking queasy*

Can you please put a PG-22…I mean MG (Mathteacher Guidance required) label on such posts? I think my brain may be damaged for good. I just couldn’t tear my eyes away from this post…like a wound you just have to see. Wanna know why?

I always had to draw figures on lines notebooks.

I hate Maths.

I HATE geometry.

My dad just got me those Dux compasses in a box. I never had a geometry box.

I was never allowed to have an ink eraser. My mother said there is no room for mistakes; I should just be careful with my work.

How do you think this post makes me feel?

*wipes away a tear*


Nov 14, 2008 at 5:59 am

Oh, and can you see a sad face inside the circle? Tilt your head 45 degrees to the right…there’s actually a sad face in there.

Oh and just for the record, I use the commando approach all the time. A smile can rub away a lot of lines and people let you draw new ones. Its rare it doesn’t work for me. But yeah, sometimes… it just doesn’t.

Why is this post making me feel so sad?

I blame that sad face. Its sending messages to my subconscious.


Nov 14, 2008 at 6:28 am

Okay, its starting to look like a dead face now because it has little crosses in place of eyes.

I think I should go away now. Its just that the diagram is so morbidly fascinating.

*stares at it some more*


Nov 14, 2008 at 9:30 am

Ordinary Girl,
Aha! Another geometry lover! And let’s see… you are still friends with your kindergarten BFF, you have every result card in your academic career saved with you, and you have an old Dux compass which is still accurate. You don’t aspire to be a museum curator, do you? :D

Ahem. Point noted. (I don’t like advanced math either. Just saying.)

Haha! You wouldn’t have failed too many times; commando method also makes you learn.

Dinky Mind,
I didn’t have a blog when you were in sixth grade, Dinky sister, so you wouldn’t have been able to apply the commando method anyway. A word of caution before teaching it to your bro: it’s not as easy as it looks!

LOL! Wouldn’t have expected less from you, buddy! What’s a sleeper hole, by the way?

Hacking all those physics exams sure used to be fun. I like your commando approach of dealing with the MCQ’s. Neat. And even neater is the way you dealt with the pendulum experiment. (I never liked those pendulum experiments. The damn thread always used to mess it up for me.)

Ahem. Point noted, again. But the post is more about just math, you know.

I don’t know if I’ll be able to reply to your comments. I am laughing too hard. :D

You know what, those ink erasers were banned in my school as well. And obviously that meant that everybody had one. Dux ink erasers were rare though.

But why do you HATE geometry? You found a sad/dead face inside an incircle; think of all the fun you can have with other geometric figures. (Though I can’t help wondering how you’ll perform at a Rorschach inkblot test if you can find a dead face inside a simple incircle.) By the way, I tilted my head towards right and I couldn’t make out the sad face. I tried finding the dead face, and I found it. Then I laughed for a whole minute.

And I like your version of the commando method too. I knew this term was going to be highly general-purpose.

By the way, if you like, I can send you a large montage of all these figures. You can then set it as your computer desktop’s wallpaper and stare at it all you want.

Qadeer Ahmad

Nov 14, 2008 at 10:14 am

I could only make the angle of 60. I was unable to understand how to make other angles. My teacher’s fault, probably ;)

Qadeer Ahmad

Nov 14, 2008 at 10:16 am

Would you like to add my blog to your Links list?
I have added yours in my blogroll.


Nov 14, 2008 at 10:42 am

That was the most passionate piece of writing I have ever read about a … umm … errr geometry!!!!


Nov 14, 2008 at 5:52 pm

Eww, no thanks. I won’t be able to move from in front of that desktop. Not that I usually move from in front of the computer, but you know, I can’t stop staring at them.

Oh, by the way, there’s something here for you in the answer to question 7. Keep blogging away, man!

Ordinary Girl

Nov 15, 2008 at 12:29 am

Museum curator?! Ahem, I would, if I could only make out what Mona Lisa was smiling about! :P

We two seem the only geometry lovers! :S Man, it makes me more attached to my Dux red compass…


Nov 15, 2008 at 9:17 am

If I were your classfellow, I would have told you how to use a protractor to apply the commando method. ;) Thanks for the link.

*grins* Actually, it talks more passionately about how to cheat in geometry.

Haha, as you wish. And thanks a lot!

Ordinary Girl,
Mona Lisa? Who said anything about becoming an art museum curator? :P Oh, and don’t get too attached to your compass… might be dangerous…


Nov 15, 2008 at 9:37 am

a sleeper hole is a lock they used in wwf to make the opponent pass out… :D

And cheating in papers is so much fun, even if you dont need to, just for the sheer pleasure of it… ;)


Nov 15, 2008 at 12:37 pm

*waits for something more social-sciency rather than mathy*


Nov 15, 2008 at 7:19 pm

Haha, I see! Yes, the commando method is extremely effective for sleeping as well, while being non-violent at the same time. As for cheating… you said it. ;)

*chuckles and apologizes* You might have to wait for quite some time.


Nov 19, 2008 at 1:49 am

Oh man! I feel so old. Its been eons since I did anything to do with Mathematics. Understandable, when you factor in the fact that my overall grade in SSC came out as an A if you did not count mathematics – mathematics alone pulled it down. And I scored that bad in Mathematics despite my obvious comfort at working with variables.


Loved the post though, and loved Specs’ comment about how well an arc called smile can work at erasing and redrawing lines.

Now, about why I felt so old after reading your post and the ensuing comments… because all that mention of critical angles, pendulum experiments, refractive indices, and optics brings back a vague recollection of time spent in the physics lab., but no real memories. It has been THAT long since.

I should go buy a walking stick.


Nov 19, 2008 at 10:20 am

Lol! Reminds me of my own Engineering Drawing class. *shudders*
I hated drawing. Which is ironic, since as part of my current job, I have to review engineering drawings a lot. And these drawings aren’t circles-in-triangles, I tell you! There’s very little you can erase and re-draw :P

Oh but our instructor was a very.. colorful guy. He once told us to re-use the tape that we used to stick the drawing sheets to the drawing boards, and this guy in the front row said “Sir, Memon mein huun!” :P

Hira S.

Nov 19, 2008 at 11:38 am

Try drawing nudes.

Fat hairy men just kill you from inside.


Nov 19, 2008 at 4:27 pm

SSC was the only time when maths saved me. HSSC and beyond were like talking to a buddy who doesn’t wanna talk.

And you don’t need a walking stick. Not yet. As long as the mention of pendulums and optics keeps ringing a bell, you are perfectly fine. Who cares about the details; vague memories like these are more than enough to make us smile.

Haha, as long as you are not the one drawing them, it’s all good. In fact, hating them gives you an edge while reviewing them: you can instantly spot a bad drawing because probably in your hatred, you would have drawn it in the same bad manner. :P But I am sure there are ways of applying the commando method on those drawings — all you need is a little creativity. ;)

LOL at “Memon mein hon!:D

You’ve tried drawing nudes?! :shock:


Nov 20, 2008 at 1:46 pm

Man I still remember the first time I studied Geometry. We had a whole new copy for it and my sole aim at that time was to keep it really neat and tidy and draw on it with my “awesome” geometry box. That was a really exciting time for me. Of course, fourteen years later it appears to be pretty stupid! :D

@Hira: You’ve tried drawing fat, hairy nude men?


Nov 20, 2008 at 3:16 pm

Haha, yeah, I remember being a neat freak with my geometry figures as well. I didn’t have a new copy for it, but the existing math one was already full of so many crosses that I couldn’t afford to create a mess out of my triangles.

And welcome aboard!


Nov 20, 2008 at 5:58 pm

Allah ka bohot shukar hai I only get to be the pain in the behind for the drafting fellows. I’m telling you, these guys make the dumbest mistakes!

Just to help out this draftsman, I gave him a drawing number from an old project just for reference. The guy just plain copied the entire drawing into the new project without changing even a single thing! Even the notes, dates, initials.. EVERYTHING!!! :P


Nov 20, 2008 at 8:29 pm

OMG … that was a fun post. I remember the geometry set of my brother which was some german brand and man … it was THE classiest compass set I’ve ever seen in my life. I used to drool all over it (metaphorically). And the day I get the privilege to use it ~ I felt like a grown up who can see world on eye level. Yup he saved it for my use.


Memories … into mathematics are lovely :)


Nov 21, 2008 at 10:10 am

The first sentence of your comment is rather ambiguous. :P And yes, naqal kay liyay bhi aqal ki zaroorat hoti hai!. My middle school math teacher used to throw this quote at us all the time.

Memories of anything are lovely. Even the bad ones, because they can’t get any worse! Your brother must have been a huge geometry set lover; even I didn’t save mine for my younger sister. But yes, using a new, er, tool — whether it’s a compass or a fountain pen — always used to make our day back then. :)


Nov 21, 2008 at 3:09 pm

very nice post,so I see you haven’t forgotten much from your school time or did you use a “commando method” for this post too?

And speaking of leading geometry sets ,I think the most tasty stationery products are done by this company


Nov 22, 2008 at 3:20 am

I kinda liked the geometry part in maths..drawing inscribed circles & arcs etc..though i absolutely hated maths..big time!
I also absolutely lurvvveddd Dux’s geometry boxes but then outa no where they just disappeared..nowadays its all COX’s market in geometry boxes & etc.


Nov 23, 2008 at 10:08 am

I have forgotten quite some things, but those that I do remember are just too interesting to forget. And thanks for sharing the link; I didn’t know about Maped.

An ILLus|On,
Practical geometry sure is fun. And right, it’s Cox these days. Hmm.

Anas Imtiaz

Nov 23, 2008 at 5:01 pm

Thank God I don’t need to use those butt-piercing tools anymore! I couldn’t even manage a nice circle at first attempt!

@Absar: Engineering Drawing, Please don’t remind! I sucked at it, managed a good paper though but my instructor lost my assignments and gave me a D!!!!! And that too crafted with a ruler and compass :@


Nov 23, 2008 at 10:13 pm

@Saadat: L(ah)ol! :P

@Anas: Lol! I loved it man! I mean, sure, all semester long I hated it! But then at the end, I got only half (when I had only done like two-thirds in the first place :P ) my semesters drawings approved, and still got a B+. Talent ki baat hoti hai :P


Nov 25, 2008 at 3:44 pm

Honestly speaking, I think if I try drawing a circle now, it will look more like an anda. It’s been THAT long that I have held a compass in my hand and drawn something.



Nov 25, 2008 at 9:46 pm

Nice name for the method… but I must say that yes, the need of the commando method arose often during school days but let me tell you, Saadat, I never cheated as accurately… =P You are one careful lad! :D


Nov 26, 2008 at 9:55 am

It’s not just a nice name; it’s a dashing name. Ironically, it was first uttered by a private tutor of a friend of mine. We adopted it for our cheating adventures. And yes, applying the commando method sure is an art — a commando is nothing if not careful. :D


Nov 28, 2008 at 3:41 am

and someone was pointing out how I havent been updating my blog? :P


Nov 28, 2008 at 9:22 am

You really need to understand how Ulta Seedha works. Unannounced hiatuses are the norm here. :P


Nov 28, 2008 at 7:02 pm

yea yea


Nov 28, 2008 at 7:03 pm

i forgot this ‘ :P


Dec 5, 2008 at 7:57 pm

Update already chotey bhai!


Dec 7, 2008 at 12:35 am

im demanding another update!!


Dec 7, 2008 at 2:53 am

update yo!


Dec 7, 2008 at 10:40 am

Bhaijan, Purple, Illusion,
Update coming on Eid, inshaAllah. :)

Dinky Mind

Dec 8, 2008 at 3:49 am

Updating bakra news on eid? :P


Dec 13, 2008 at 12:50 am

I used to do this when my circles weren’t quite perfect but by my A Level time,I learnt a handy tip: buy a compass with the lead embedded within and keep your pinky on the paper while you draw your cicle- hasn’t failed me since. Your tips are so cute though-love the nickname ‘commando method’ awesome.


Dec 13, 2008 at 2:50 pm

Dinky Mind,
Maybe. :P

Okay, now I have to try the pinky trick. Might screw up but will be fun, nonetheless. And yep, the name is awesome. Gives a very warrior feel to it.


Jan 3, 2009 at 10:03 pm

lol…sigh geometry used to be brilliant! Clean crisp lines..went through more geometry sets then ever imaginable! Btw..did you ever use that instrument that had TWO pointy sides? I never did get what it was necessary for.

to be honest when I first read the title I was thinking of the other commando method X)..and since the post lead to nowhere in terms of undergarments or lack of I decided to re-read the entire post without preconceived notions :p


Jan 4, 2009 at 12:48 pm

Good to see another geometry fan! The two pointy sides instrument is called dividers. And yep, I never did use it for anything academic either — it was only a good weapon against the enemies.

LOL at your assumption of the other commando method, which is not actually a method, but an attitude! I am glad you realized soon. :P

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