Tuesday, January 31, 2012

Discoveries in a Day

Today was pretty eventful. Our usual discussions and surfing led to three discoveries (to be precise...Observations). None of them is that significant, but still we found them to be notable. It may happen that some of you are already well aware of these facts. But for us, it's nontrivial. Hence, the post...

1. Real life application of the fact that the sequence (n+k)/n goes to 1.

Most of you must have solved age problems in school. The problem statement would be something of this type....
"A man is 4 times as old as his son. In 3 years, the father will be 3 times as old as his son will be. How old is each of them now?"
Cynosure's post on the difference between the ages of siblings reminded Deep of a question that she had in mind as a school going kid.- "Why does it happen that as the time progresses, father who was 4 times his son's age became 3 times the same son's age". Translating this question into the language of Mathematics, with son's age as 'n' and father's age as 'n+k', yields a sequence (n+k)/n which is obviously decreasing and converges to 1 as n goes to infinity.

2. Sunrise and Sunset timings

It started as a discussion with MGK on the timings of getting up. We were whining about not feeling like getting up, as it's too dark around 6.30. Out of usual habit, we googled and got the latest time for sunrise as 7.15 am, which happens to be in the second week of January. Isn't it too late for The Sun to rise at 7.15 am??? No wonder then that we petty human beings don't feel like leaving our beds. This googling led to the second interesting observation of the day - "The shortest day doesn't correspond to the latest sunrise and the earliest sunset." Again resorting to the tools of real analysis, if we define the timing of sunrise on nth day by Rn and that of sunset by Sn, the shortest day would correspond to the smallest value of (Sn-Rn). But then inf (Sn-Rn)≠inf Sn + inf (-Rn) (To be precise, argmin (Sn-Rn)≠argmin (Sn) or argmin (-Rn) ). In fact, in this case it turns out that the “n” for which the corresponding extreme values are attained (argmin), are different for all the three quantities, Sn, Rn and Sn-Rn. So, we got a good application for somewhat non-intuitive real analysis result. For actual geographical reasoning, you may google and do explain us, if you get something.

Enough of real analysis stuff now…. Let’s get to real blogging

3. “blogspot.com” changed to “blogspot.in”

Richa noticed that the Feedjit has kind of restarted, as it was showing only latest 2-3 entries instead of its usual count of 50. But, when we went to Feedjit’s “real time view” for our joint blog, it seemed perfectly alright except the fact that in last 8 hours there was only one entry and it was from Indonesia. When we tried to visit the same link via blog, it turned up that it had almost 20 entries during last 5 hours, but all of them were from India. Then we noticed the change in the link from “.com” to “.in” and realized that all the blogspot.com links are getting redirected to blogspot.in links. Googling almost instinctively, we stumbled upon the page giving the details of this country specific redirecting. This helps Google to remove the content found objectionable by a specific country from a page visible in that country only. Of course, it won’t affect the harmless content posted by ordinary people like us. But still, if you want to see the original “.com” version, just type “-----.blogspot.com/ncr” to get the no country redirect version. Dear Feedjit users, don’t get disheartened if the panel on your regular blog shows only Indian visitors. If you want to see your visitors from abroad, go to “/ncr” link given above…..

That’s enough research for today… Off to some real research now…

- Akanksha & Deep

Friday, January 27, 2012

折り紙 - Origami

Haven't written anything since long... In fact there has been a drought of posts in 2012. But there is a reason behind it. Was busy with some creative stuff apart from writing. Here is the final output of the same seen through Deep's camera..... (Click the caption for enlarged view along with the names)
Origami City
It all started when our Japanese teacher told us about the exhibition "Reflections-2012" showcasing some aspects of Japanese lifestyle and culture to be held at Ranade Institute. We were supposed to present something related to Origami. First we started with the idea of airport, but finally landed on this city. Meanwhile, there was also a chart to be prepared related to origami stories. So, with so many things to do along with the regular work, couldn't take out time for blogging....
It was really an interesting experience... to see almost real-life like objects emerging out of a plane sheet of paper, without using anything other than the paper and our hands (Not even scissors, gum etc.). The word Origami literally means folding paper (Ori = To fold, Kami= Paper). So, our city consists of just twists and folds & no destructive acts like cutting.....
Showcasing this city and explaining the types of origami, telling the stories related to it to the visitors on the actual tenrankhai (exhibition) day was even more interesting. The most enjoyable experience was to tell these things to Japanese people in chyotto chyotto Nihongo (Little bit of Japanese) and listen to their excited responses in थोडा थोडा हिंदी / थोडी थोडी मराठी. In fact I even got a 5-yen coin, which is considered to be a lucky coin in Japan, from a Japanese girl.... So, in all it was a good republic day!!!