Big mountains

I love Himalayas and have the good fortune of traveling in Himalayas. Its a feeling which has no parallel. While you travel you are constantly reminded of the Nature's grandeur. One of the two places which I would like to go back and visit are a small town named Sarahan and another small town Recongpeo in Himachal Pradesh. Ideally I would like to have a 3 or 4 month long vacation and spend time in Himalayas doing trekking and enjoying the spectacular scenery. The Himalayas, The Karakoram range and The Kunlun Range contains most of the tallest mountains. So its not very surprising that all of the top 56 mountains are shared between these three giant mountain ranges. Click here to see the list. I just learnt about Kunlun Range and naturally I am fascinated by this mountain range and could be included in the Silk route travel I have in mind. There is one great site of Piero scaruffi do check it, its pretty interesting. He has traveled to more than 95 countries, done lots of work in computer science, poetry, philosophy. Ofcourse he is a mathematician !!

The way I feel now

"He who is limping is still walking". I loved this thought because this summarizes my current situation. Yesterday I participated in Badminton Tournament and it was fun.
The news channels like CNN are ever ready to malign President Bush and this always makes me think if people are so disgusted by him then why they elected him second time ?? and also how does it matter to him if his rating is 30 percent or 5 percent. I predicted on this blog that Bush will win inspite of the ridiculous projection by these very same channel overwhelming favoring Kerry. It is fashionable to say that he is a disgrace to US but as far as I see I think Bush is going to be one of the most influential leader in our history. The people who spew vitriolic on him should ask themselves what it would be to live a life in a burqa and have no freedom of thought, any thing against the religion or its authority could be termed blasphemy and lead to being stoned or maimed. Its a hate ideology and the war on terror brings that issue to limelight. Ofcourse the military method wouldn't bring the solution but then currently its the only method which is sanctioned. Why can't we boycott and force these countries like we did to South Africa in apartheid era. Because here also we have the very same situation. People get tortured and always live a life in constant fear always judging themselves if their slightest act would carry them to the hell fire. I remember visiting Malaysia once and was surprised by so many prayer halls everywhere. Its good to do prayer as it brings calmness but if something is made a routine you have to adhere at all cost just to avoid hell fire then it becomes agonizing and that's the reason these people start hating others who live and enjoy life without having to do such chores. They can only assuage their hurt feeling by telling themselves of the heavenly pleasure they will have and the others will be forsaken and so you have an army of suicide bombers ever ready to explode themselves to get out of this jittery and enjoy the eternal bliss so promised. Freedom of thought and freedom to practice and choose ones belief has made America one great nation and this should be sustained and carried forward by the media instead of imposing on the public with their own shallow researched opinion and adhering to political correctness.

Kinder Bueno

Its early morning now 5:14 AM by the watch on the extreme right hand corner of my computer screen. I am enjoying this chocolate and its delicious. Ever since I have started eating lots of fruits in the morning I have been able to control my intake of chocolates by substituting it with other fruits. However I do love chocolates and so these days I try for the exotic ones. Its only when I thought of posting this blog I tried to find out more about this chocolate and it was a happy surprise to discover that its a Danish chocolate ! Ever since the cartoon controversy I admire Danes for their courage and resoluteness in defending freedom of speech.

A promise not yet fulfilled

In 2001 I visited Nainital in India. As any tourist I was busy capturing as many moments humanly possible. There was this guy Kamal who gave me the sail boat tour, his son was also on the boat and naturally I took some snaps of him. Kamal insisted that I write his address and should send him his son's picture. Later back in New Delhi I had the pictures but almost forgot to send him though not quite even though the address was always in my wallet. Mind you I changed several wallets but each time his address also made his way in to the new wallet. I even once lost my wallet in Singapore but as luck would have it I did find it later at the lost and recover office. About six months ago I emptied out much of the junk from my wallet into my drawer, today while searching for the pencil leads I first discovered the half of the address and later the other half. I am ecstasic because a week before I was thinking about it. So to make it permanent I am posting this address on my blog so that someday when I go back to Nainital I meet Kamal and his son and surprise him by the long held promise which I still haven't forgotten. Here is the address
Kamal
Balrampur Outhouse
Post Office Mallital
Nainital
Pincode 26301

Pi Mu Epsilon and SIUC cardboard boat regatta

On 11th of April I got a mail from Dr. Hughes that I have been invited for the Mathematics honors society. I love it and look forward to the joining ceremony to be held sometime in May. I seems that I don't have to do anything else like building a card board boat I did with my fellow Tau Beta Pi (engineering honors society) members. It was fun and a great learning experience. To an uninitiated even thinking of a boat made out of cardboard and people sitting in it might sound preposterous but come on the day of race and you are bewitched by plethora of well crafted nubile floaters. I hope this year I will be able to find some time to enjoy that wonderful event that very much epitomes a professor's dedication to make learning fun for his students.

Collinear intersection of tangents

This interesting problem was to show that if there are 3 circles and each have a pair of common tangents to other the intersection of the 3 intersecting pt lies on a line. The challenge was to draw 3 circles and then draw tangents. It becomes interesting when one starts with two circles. Since its pretty easy to start with a line and then make two circles on it which will always remain tangent, no matter how you change the shape. The second tangent can be drawn pretty easily by reflecting. However incorporating the third circle such that one can draw parallel tangents was giving me problem. I had a good discussion with Dr. Kocik regarding this. Yesterday around 3:am as I was about to goto bed (inspite of promising myself to go to bed early) I had an idea why not draw a triangle first and then draw circles inside it in this way I start with each of the 3 circle having a pair of tangents and all I would then need is to draw the 2nd tangent which my intuition said would be easy and after a 20 minute bout with KIG. I had the drawing working perfectly. I repeated it again on GeoGebra and it came out nicely. In the morning I tried on KSEG and this is the output. I have hided the clutter so you can see the nice geometry.

3 circles mutually tangent to each other

I was trying to draw 3 circles mutually tangent to each other in context of understanding the Descarte's theorem which give rise to Appolinius Gasket. First Descarte's theorem. It says that if there are 3 kissing circles than there exists two circles which kiss all these 3 circles and the curvature has a beautiful formula (b1+b2+b3+b4)^2 = 2(b1^2+b2^2+b3^2+b4^2) where b4 gives two values and hence two circles. One can solve for b4 and after some yuckky algebra it can be shown that its b4 =(b1+b2+b3) +-2(b1.b2+b2.b3+b3.b1)^(1/2). The cool thing about Apollinian Gasket is that the whole gasket can be inverted into itself. Sort of infinite reflection when two parallel mirrors are placed. and then the two roots of quadratic can be expressed more easily as d1 = 2(b1+b2+b3)-d2
It has interesting history behind it because people didn't find the last form for almost 200 yrs. Here is the attached file which shows how one can draw 3 kissing circles. Drawing two kissing circles is straightward. To draw the 3 draw an arbitrary circle centred on any one circle and then the difference b/w this and arbitrary circle should be added to the other circle. the intersection of these two will give you pair of pts which will be equidistant from the original 2 circles and now one can draw a 3rd circle kissing the other two.

Not much to say

I just came back to Math lab after my Physiology class. I have a dinner to attend today (RSO dinner at ball room in Student Centre) and a test on Plant Biology due tomorrow, besides that I have to study for my coming Geometry test and do the homework. Haven't touched Fourier for some time so now I should be doing it with more enthusiasm.
This Sunday I went to India Night. The food was good and it was well organized. I think I can definitely do a great job with it and should organize it next time.

Reading Wiki and CIA

I have owned stamp of Cyprus since I was 12 yrs old. I still remember that red stamp now pasted in my "Rita Stamp Book". I bought for myself in Kamla Nagar. Out of curiosity today I searched for Mediterranean on wiki and Cyprus caught my attention. I now know that Mediterranean sea is almost land locked among Africa and Europe and Asia. The good part was knowing about Cyprus. A small island country that is rapidly growing. I now want to visit Cyprus and take a Mediterranean Cruise !! The southern Cyprus is faster growing compared to Northern Cyprus which is controlled by Turkey and its recognized as a separate country by Turkish people. The merging of two parts is being pursued but still hasn't happened and I think it won't be easy because of Muslim people's way to differentiate themselves from non Muslim people.
On my last trip to California I met Kamina Singh an Indian girl settled in New York whose family had migrated to Guyana in South America. She was one heck of a girl who took the Trans Continental Train Journey just for the experience of this wonderful ride and had plan to go back to New York the very same night we were supposed to reach California. So today I also searched for Guyana and found out that its French Guyana and is part of France. The thing which astounded me was the number of child borne per women to be 3.1 ! Guyana is pretty famous of the Korou launch site. The EU launches its space shuttles from this wonderful country. I definitely will visit Guyana sometime.
Today also on CNN present I watched a documentary on Mary Magdalene. It was interesting and anyone who has read the Vinci Code will find it interesting. It explored how Mary Magdalene came to be known as woman associated with world's oldest profession (Sorry for verbosity) when now there are evidences and speculations that she might be a ordinary woman and may be the church is hiding something. Whatever be it, I think the Churches have reformed in many ways for the better and today you can find some of the most gentle and compassionate people from church groups.

Thoughts to think and ponder

Recently while scurrying through books at the walmart. I came across this wonderful thought by David Gayson.

" We fail far more often by timidity than by over-daring "

and another one I found on thinkexist website by Lord Byron
"Those who will not reason, are bigots, those who cannot , are fools, and those who dare not are slaves"