How Many Triangles?

Here’s a question: Take an equilateral triangle ( △) and make 4 (and only 4; 5 or more should be impossible!) triangles out of it by drawing a few lines in its interior such that at least one edge is common to each pair of  these 4 triangles!

This problem has two solutions: One has a trick to it and the other one is straightforward. The tricky one is easy to find but finding the straightforward one requires thinking out of the box as one of my friends put it!

Here’s the thought process that leads to both of these solutions:

This video is ‘inspired’ by this video titled Metamorphosis of the Cube.

During the making of my ‘trigon’ video, I started thinking about 3D rotations and found a very concise (and hence, beautiful!) solution to a problem. A ‘problem’ which I had encountered while going through the chapter ‘Spinors’ in Misner, Thorne & Wheeler’s Gravitation about 3 years back! That chapter does have the solution but somewhy I never got comfortable with it! To get to know the problem and the solution, head to the post on my Physics’ blog:

3D Rotations

Baby, Please Kill Me!

If you don’t know what I’m going to talk about, keep on reading!

† Since scanlators at Musashi Quality are busy NOT working on Sketchbook, I instinctively got an urge to check out a new 4-panel style manga! And this manga came in the form of Baby, Please Kill Me! “It must be a romantic thriller comedy” is what I thought when I read the name of this manga but boy oh boy, was I Wrong or was I wrong! Here is the summary of BPKM from OneManga:

It's a 4-panel style manga that follows the comedic life of a typical school girl Yasuna and her assassin classmate Sonya. Sonya’s attempt to fit in often fails when her natural assassin instincts kick in and Yasuna’s attempt to be more friendly with Sonya often gets her hurt or intimidated.

“What the hell is this?” is what I thought when I finished reading the above paragraph. “But what the hell, I’ll read it anyway” is what I thought next! I’m glad that I read the couple of chapters available then and now that I’ve read the 14 chapters of Volume 1, I’m awaiting the second volume… :) Believe me, the humour in here is not as subtle (or abstract) as Sketchbook (as many people seem to believe!) so I guess people with much-less-refined senses will also be able to enjoy BPKM. Do check it out!

♫ I also started seeing Nodame Cantabile again. This is not a confession. I did not watch the episodes I had already watched. Apparently, there are 2 more seasons consisting of 11 episodes each about which I didn't know till a few weeks back! I had watched the first season consisting of 23 episodes during my stay at KGP. So, I was thrilled to know that there are 22 more episodes to go. Here is an abridged synopsis of NC taken from Wikipedia:

The series depicts the relationship between two aspiring classical musicians, Megumi "Nodame" Noda and Shinichi Chiaki, as university students and after graduation… Nodame is an extremely talented pianist who wants to be a preschool teacher… She is messy and disorganized, takes baths several days apart and loves to eat… Chiaki is talented in piano and violin and has secret ambitions to become a conductor. An arrogant multi-lingual perfectionist… They meet by accident. Nodame quickly falls in love, but it takes much longer for Chiaki to even begin to appreciate Nodame's unusual qualities.

This is one of the few animes whose manga I’ve not read (others being Samurai Deeper Kyo, etc!). One of the main reasons I’ve not read Nodame Cantabile is because this series is supposed to be about Music and you can’t hear this music while reading, now can you? You need to have a sound medium to hear music. That’s where anime comes, having the sight & sound advantage over manga! Also, words like Mukyaaaa & Gyaboooo make sense when you hear them… :) If you’ve ever wondered whether people with opposing personalities can interact favorably with each other or not and if yes, how would it look like to an outsider – this is the right anime (or manga) for you! That’s all I’ve to say to sell this anime…

⊛ During summer, there are not many ‘good’ TV shows around to watch. So, if you are looking around for a good show to watch during this summer, may I recommend  one of the best stories ever told in the form of a(n) manga(/anime) called Fullmetal Alchemist(: Brotherhood). When I first started the draft of this post last week, I had not included manga in the previous line. So you have the right to ask why did I change my mind in a span of less than 7 days. It may not be  that obvious, but FMA manga’s author has dropped the ‘THE END’ – Bomb on us! Before I rant a bit more, here is some info about FMA(:B) from YouTube:

Brothers Edward and Alphonse Elric’s reckless defiance of alchemy’s Law of Equivalent Exchange resulted in no miraculous reunion with their mother, but a hellish nightmare; half of Ed’s limbs were torn from his body, and Al awoke to discover his young soul transferred to a suit of armor…

If this short intro does not give you enough motivation to go find the anime / manga and watch / read them as fast as you can, I don’t know what will! Anyway, the anime is still going strong following the manga pretty close. As I said, the manga has ended this month, so the anime should also be over in 4-5 more episodes. The last chapter of FMA was more than 100 pages long and the end was quite good (at least I was satisfied!)… not those everyone-lived-happily-ever-after kind of endings but life-goes-on kind of endings where the sketch of what everyone is going to do about it is outlined! Thus, this manga has a slightly different ending (in spirit) than the other two mangas – Inuyasha & Elfen Lied, which also ended after I’d started reading them. I do not want to discuss the ending of FMA any more than what I’ve already said… :)

So, I will just leave you with a

List of Anime & Manga I’ve seen & read

Walking in the Footsteps of…

… Nagisa Kurihara (the Miracle Girl).

Before that, let me just say that I felt excited today while grocery shopping like Hazuki usually feels! Basically, my shopping cost exactly $\$35.00$ and I ‘saved’ exactly $\$3.50$ due to discounts on the prices of 3 items!

Anyway, let us get back to walking… So, if you read Sketchbook (which I seriously DOUBT!) then you know that Kurihara-Senpai is

An inquisitive but easy-going girl with keen biological interests. Kurihara's knowledge of this field is literally encyclopedic, in the sense that it is only limited by what appears in scientific encyclopedias. She identifies and interacts with a variety of plant and animal life, sharing some of their unique characteristics with other club members and with the audience. [copied from Wikipedia]

Last week, I had an opportunity to visit Ashley Schiff Park Preserve on-campus. It was a tour guided by a Botanist (Margarita, I guess) and Pat (not just a Botanist, I guess!). Learned (or rather got familiar with) a few things like the facts that:

• Leaves of some plants (like Sassafras) are highly fragrant;
• Certain plants (Moss) / insects (Gall Wasps) have weird life / reproduction (including alternating sexual & asexual generations) cycles;
• Leaves can also get bitten by insects in response to which they develop bumps (like us) called galls;
• Berries (red ones!) / Flowers (tulips) can be there where you don’t expect them to be;
• There are two types of Solomon Seal plants: True(?) & False(!);
• Insects camouflage themselves a little too well.

Anyway, that’s all I want to share about that trip for now. Check out the Preserve below:

ASPP

Casio Exilim Z2000

Nothing much to talk about since last post. Spring Semester is over now. People are getting married. Have to shift to a new room by the end of this month. People are afraid to die. We are ignoring each other. Summer Research awaits! Yet people do die. Manifest summer has arrived. Should plan for the moving-out-event. There’ve been a bit too many earthquakes. Muted excitement with hypocrisy thrives well. Ok, she more than me. Went to The Store after a long time. People feel good (b(s(?))ad) after analyzing me. Mixing with groups without projecting yourself as a jerk is tough. I feel relieved after knowing we’ve still a long way to go!

Anyway, I bought a new camera mentioned in the title sometime in April. Some of its impressive features to me are:

1. 14.1MegaPixels, 5x Optical zoom
2. 3” super clear LCD screen
3. EXILIM Engine 5.0
4. Image Stabilization (both Hand shake & ‘Subject shake’)
5. Premium Auto including other Best Shot (BS) scenes / modes
6. Face/Smile Detection, Motion Detection, etc
7. Intelligent Auto-Focus (iAF)
8. Light-weight (~150g)

Let us look at what EX-Z2000 can do now. All the following photos are hyperlinked to original full-size ones which open in a new tab (if your browser supports tabs and if your browser settings are not too weird). [If you did not know that the hyperlinks in my posts except the end-of-the-post-link open in new tabs, I am not surprised! Also, if you think that all my posts have an end-of-the-post-link, you are not doing me any favours!] Or you can download them (by right-clicking on them and looking for an option close to ‘Save’ in the context menu) and look at them at leisure. Play around with them by zooming, cropping, etc if you have more than the standard time, usual mortals have. Here we go:

14MP at work

5x Zoom at work

Most of these photos are shot in Auto mode. Some in Premium Auto (PA) mode which basically ‘recognizes’ other BS scenes and optimizes for the scene (like Portrait, Scenery, Macro, Greenery, Sky, etc) in front of the camera. The following are shot using PA mode and it shot them in Macro & Macro+Greenery modes. [The camera takes a while (~5-10 sec) after the image is shot to process it and save it to the memory card, though!]

Zoom demo: Almost none –> Mid-way –> Full 5x

Faithful colour reproduction

 

I do not have much experience (well, none!) at shooting photos but when it shows blueness of the sky and whiteness of the clouds while maintaining crispness of other colours, I say the camera is doing an awesome job. The lower twin photos are shot in Auto & PA modes respectively (from L to R!). You can form you own opinions about their qualities.

CCD Shift Stabilization at work

 

I’ve to admit CCD SS is on in both the photos but the thing to note is that the flower was swaying ‘violently’ (peak-to-peak amplitude: ~5cm) on the left and ‘modestly’ (peak-to-peak amplitude: ~2cm) on the right because it was windy that day. And the result is that the blur is ‘barely’ visible on the left while there is ‘none’ on the right! More photos of the tulips:

 

This is the view from my office in Math Tower.

Stitching a couple of ‘well-shot’ photos is a breeze via MICE (Microsoft Image Composite Editor). Sadly, there is no built-in mode for stitching photos together on the camera itself. Other cameras (I think Panasonic, Sony, etc) have a Sweep Panorama mode which is really nice. [I think I’ll get one of those too!]

One stand-out BS mode is “Business cards and documents”:

The idea is you take a shot of some document (like on the left) and the camera corrects for the angles, projections, etc and you get a ‘corrected’ rectangular photo (like on the right)! [Ok, I am cheating a bit here, the camera did not recognize the ‘correct’ right side boundary because it is not sharp enough compared to the other three boundaries so I cropped the photo manually.]

The web does not have the list of all the 40 Best Shot scenes / modes on EX-Z2000 (well, I could not find it!). So I’m going to put it here for those who may search for it while researching on cameras and also because it may increase the traffic on my blog (one of the blogger’s optimistic dreams). So here goes nothing:

1. Auto
2. Premium Auto
3. Dynamic Photo
4. Portrait
5. Scenery
6. Portrait with Scenery
7. Children
8. Sports
9. Candlelight Portrait
10. Party
11. Pet
12. Flower
13. Natural Green
14. Autumn Leaves
15. Soft Flowing Water
16. Splashing Water
17. Sundown
18. Night Scene
19. Night Scene Portrait
20. Fireworks
21. Food
22. Text
23. Collection
24. For eBay
25. Backlight
26. High Sensitivity
27. Oil Painting
28. Crayon
29. Water Color
30. Monochrome
31. Retro
32. Twilight
33. Multi-motion Image
34. ID Photo
35. Business cards and documents
36. White board, etc.
37. Silent
38. Prerecord (Movie)
39. For YouTube
40. Voice Recording

Now we settle into comparing-two-cameras mode. No external photo editing has been done in the following photos for comparison purposes. The comparison is between my ‘old’ camera, Casio Exilim Z4 (4MP with 3x zoom) and my ‘new’ camera, Casio Exilim Z2000 (14MP with 5x zoom). Click on these photos to compare them on your own.

 

Both these photos were shot via BS Scenery scene. The photo taken with Z2000 had its Image Quality set to Normal whereas Z4 had been set to Fine Image Quality. Do take note of at least these things: the colour of the sky, overall colour composition, details in the photo (you can actually read the license plate number on the black car in the right photo!) and the achievable level of zoom.

 

These are (roughly) 3x zoomed versions of the above photos. Do take note of the reducing clarity (graininess?) in Z4 already at the original size whereas Z2000 has not lost any yet. In fact, it does not loose much clarity even at 5x zoom.

That’s it for today. Quite a long post in quite a while. I will leave you with other photos I shot while going to my office from my apartment on a Sunday:

On-Campus Sites

Overheard, Misheard & Unheard offs-II

This post is a collection of a few unrelated lines so I’ll just group them into two sections with no clear, coherent narrative binding any of them together unlike the last one.

OMUs 5

“Heard the phrases on the left but then realized what was actually said on the right:

Thank you Dharmesh! –> Thank you Very much!

Are you a girl? –> Are you enrolled?

Heard someone say to his friend (I guess!): You can marry someone you know, but you are not doing that, are you?

Saw a car’s license plate labelled: HECK 1”

OMUs 6

“Long-awaited scanlations of Sketchbook Volume 6 have started. Not many people in my near vicinity read or understand this subtlety (or nuance, if you will) of a manga known as Sketchbook. Someone great has conferred upon Sketchbook the title of ‘The Purest Manga Ever’. That was why I was left flabbergasted when one of my friends suggested that I may be thinking of Sketchbook during a conversation which was let’s just say ‘not that pure’! Obviously, ‘nobody’ understands the precise definition of what ‘pure’ means in this context (or in any context for that matter!) because one cannot say something is good before specifying (or implying) what constitutes as bad (or vice-versa)! So just for the heck of it, I’ll pretend to compare ‘Sketchbook’ with ‘Hidamari Sketch’:

Sketchbook

 

Hidamari Sketch

.”

So that’s all. For a much ‘better comparison’, check out the one minute (~18:00-19:00) of

Sketchbook ~Full Color’s~ Episode 13*

*The audio & video seem to be out of sync, so mute the audio and concentrate on the subtitles!

Happy April Fool’s Day

I was going to put up a link to a paper on this auspicious day but unfortunately arXiv.org didn’t co-operate and the paper is ‘on hold’. So, this now turns out to be a ‘bogus’ post.

Well, that paper was more or less woven around these videos, so just have a look at them and do take a note of their titles:

CG of E8xE8 Part-I

CG of E8xE8 Part-II

+ - Shaped Billiard Table

BECs

Teleportation

Star Formation

4-Point Scattering

Well, hope you enjoyed these videos… You can also have a look at the paper below, though :)

Parody Paper

T(w)o ‘thon’ or No(t) t(w)o ‘thon’

The days are passing quietly without much happening, which in itself is a bad sign. On top of that, I got entangled in a dumb squabble last week with AG (one of the friends who came to see me off here) concerning the existence of a numerical suffix ‘-ठों’ in Hindi!

The story is simple: I usually add the above-mentioned suffix to a number to stress multiplicity (like ‘n-fold’) as in दो-ठों (two-of-them). But when AG heard ‘-ठों’ uttered more than once, he could not contain his confusion, giggled and asked: What the hell is ‘-ठों’? I was as confused as he was and shot back: What the hell kind of question is that? And that’s day one of the confusion.

Next day, we were leaving the department to have lunch and he brought up ‘-ठों’ and stressed that it is NOT a Hindi ‘word’. And I stressed it IS! After too much stressing from both sides, it got stressful and we agreed to ask some other Indians around, then and there. (Just for some dramatic effects: It was drizzling then and sorting out this lingual debate was such a ‘high’ priority that) He called one (Source G*) and I called two (Source A & Source S). [It is also interesting to note that he called someone on-campus and I called people way out-of-campus!] Anyway, his ‘accomplice’ agreed with him and my ‘accomplices’ ‘agreed’ with me!

I write the second agreed in ‘inverted commas’ because my Sources confirmed that they have heard ‘-ठों’ used (and they themselves use it!) but added that it is at best a colloquial / regional construct; not an ‘authentic’ part of the Hindi language… (Oh yeah, that much is certain with no reasonable doubt now!)

So after day two, I still use ‘एन-ठों’ (n-of-them!) in Hindi conversations and AG still giggles at its use!

Finally, I’ll leave you with my website’s new address:

JKMSMKJ

*SG has made his first appearance on my blog in this post so no links available to use!

Happy (Belated) Holi

होलीको उपलक्ष्यमा तपाईंलाई हार्दिक शुभकामना!

होली मुबारक हो आपको!

OK, this post is 2-3 days (depending on whether you’re in Nepal or India) late but I had to do some brain-storming in order to compile some material for this post. I did not just want to post the answers to the last post’s questions! Now a couple of days after Holi, I do have some extra material… But before we get to that, let me give you the much-awaited (whoever was waiting for these should probably ‘Get A Life’) answers:

1) 2 (1)

2) D (1)

3) E (1)

4) D requires ‘e –> a’ while others require ‘el –> le’ to form ‘common’ words! (1) E should have had ‘quad’. (1)

5) No/Yes, I don’t care. (0) [But, I would like to see a sensible extension! :)]

…which is translation of a stanza (from a poem I guess!) penned by Ashok Chakradhar. The usual comments about accuracy, etc of translations of shers apply to this piece also! (Look at my earlier posts for details by searching for shayari… I don’t feel like linking to those again!) Here it goes:

जो मेहनत करी, तेरा पेशा रहेगा,
न रेशम सही, तेरा रेशा रहेगा।
अभी करले पूरे, सभी काम अपने,
तू क्या सोचता है, हमेशा रहेगा।
-अशोक चक्रधर

Jo Mehnat kari, tera Pesha rahega,
Na Resham sahi, tera Resha rahega|
Abhi karle pure, sabhi Kaam apne,
Tu kya sochta hai, Hamesha rahega|
-Ashok Chakradhar

Hard Work, keeps your Job,
Not Silk, at least your Essence.
Complete Now, all your Tasks,
Or do you hope, of Permanence?
-Ashok Chakradhar

For those who are wondering about the ‘Answers’ in this post, here are the

Questions

Multiple Choice Questions

1) How many of the prizes below are real?    

A. Nobel Prize

B. Abel Prize

C. Bibel Prize

D. Tribel Prize

E. Quabbel Prize

2) Which one of the above is odd-one-out?    

3) Which one of the above is odd-one-out in a different context?    

4) Mention both the contexts.

 

5) Can you consistently extend the above prize list? If yes, do it.

 

 

Answers