The Bird of Crimson and Gold Jawahara,

What talent! You have transformed the ordinary into something extraordinary. I enjoyed reading it very much.

Fozia

chowk@two
Happy B`Day Chowkwallas and congratulations on another year of good work.

Fozia

12th Man Reports This was very hilarious! Some of my favorites nuggets:

``Rule 17-z (Section CVII) explicitly requires that batsmen hit all quadrants of the ball with equal probability..…``
:-) :-)
``Speaking from behind a stall door in the men`s room at Headingley``
``the English team and other old ladies` groups``

Is another `report` forthcoming?

Fozia Qazi

An MD’s Version of Faiz Nice! Reminds me of the following parody of Adam(writer unknown)

meN hospital ki ra:h se: ho kar guzar gaya:
varna safar haya:t ka: ka:fi: tavi:l tha:

Fozia

Mathematics with Minimum Raw Material, Part 2 In my last reply I should have said ‘sides’ instead of ‘areas’ . Oops!

Fozia

Mathematics with Minimum Raw Material, Part 2 Re: Wasiq and the dissection of a square

Not sure if you`ll read this since this article is off the front page now, but I saw a dissection of the square today in the hallway leading to my office! Talk about coincidences :) It was posted on the wall by a colleague of mine who is away at present. He has a habit of posting such problems on the board for our amusement and must have done that before the semester break. I didn’t get a chance to look at it until today. Anyway, it is a clever dissection with a total of 24 squares. To get you started call the square abcd
and divide each side into 175 units.
Along side ab are squares of areas 64, 33, 35 and 43 ( in that order)
Along side bc ….43, 51 and 81
Along cd 81, 39 and 55
Along da 55, 56 and 64

The gap in the middle is filled by 15 other squares having areas 1, 2, 3, 4, 5, 8, 9, 14, 16, 18, 20, 29, 30, 31and 38

I don’t have the source, but I can check with my colleague once he comes back.

Fozia

Mathematics with Minimum Raw Material, Part 2 Re: Wasiq(16)

Very nice proof! Now I must find the first one.

Yes, I did check the pi algorithm. For me though, the digit hunt itself is not very interesting ( I lost interest in it after two decimals places :) ). What I find fascinating about pi is its unexpected occurrence in myriad mathematical situations.

Fozia

Mathematics with Minimum Raw Material, Part 2 Re: Goga(13)
Just read your query about women mathematicians. There are a few. I had already mentioned Emmy Noether Other names that come to mind are Hypatia, Sofia Kovalovskaya (sp?) and Sophie Germaine (amongst the dead mathematicians). Amongst the living - Ingrid Daubachies, Cathleen Morawetz and Mary Ellen Rudin to name a few.

Sophie Germaine’s story is quite interesting. As a child she was not allowed to pursue mathematical studies because of her gender, so, at night, she used to sneak math books from her father’s library into her bedroom to read. When her parents found out they took away her candles (and I believe her nightclothes as well so she wouldn’t venture out at night again!) But she persisted and became a very good mathematician. She had to initially publish her work under a male pseudonym but eventually found recognition. Hats off to her courage!

I remember reading somewhere that Pythagoras’ wife was also a mathematician and carried on his school after his death so she might be regarded as one the first known women mathematicians.

Fozia

Mathematics with Minimum Raw Material, Part 2 Since we are naming names don’t forget Cantor and Noether and I agree Al-Khwarizimi also belongs to this club.There are two other Greek mathematicians who deserve mention – Eudoxes and Hippocrates (not the one related to medicine). Eudoxes’ method of exhaustion for finding areas can be regarded as the precursor of the notion of limits. He also rescued Greek mathematics from its ‘logical scandal’ by his theory of proportions. I would rank him higher than Pythagoras.

Re: Wasiq(9)
No, I have not come across any such proof but it sounds interesting. Do you have the proof for (2) ?
Re Goga(8)
Ah, but mathematicians are not concerned about such trivial ‘realities’.

Fozia

Mathematics with Minimum Raw Material, Part 2 Re: Khan

I don’t think there are any clear winners in either category but if I had to pick I’d choose Euler and Gauss amongst the mathematicians. In the second category I’d vote for the Greeks simply because their logical rigor provided the foundation on which other giants could build.

Re: Wasiq

Yes, Cantor and part III it should be.

Here is an appetizing application of Pythagoras theorem.

A large pizza costs the same as a medium and small combination. You have to decide whether to buy the large pizza or the medium & small combo. What should you do?

Answer: Cut each pizza in half (so that you have three semi-circles) and arrange them so that the diameters form a triangle. If it is an acute angled triangle then choose the medium & small combo, if one of the angles is obtuse then choose the large pizza and in the event that the triangle is right angled then either choice is equally good (or bad if you are into healthy food!).

Reason: Let us say the three diameters are dl, dm and ds with respective areas as Al, Am, and As

If the triangle is right angled, then

sq(dl)=sq(dm)+sq(ds)

or (pi/4) x sq(dl)= (pi/4) x sq(dm)+ (pi/4) x sq(ds)

and so Al=Am+As

If the triangle is acute angled, then

sq(dl) *is less than * sq(dm)+sq(ds)

etc.

Fozia

Mathematics with Minimum Raw Material, Part 2 Thanks for posting this. Euclid`s proof of the infinitude of primes and Cantor`s demonstration of the countability of rational numbers are two of the most elegant yet simple proofs in all of mathematics.

Interested folks may want to try the following...
.... cut a Mobius Strip lengthwise all the way around. You will be surprised with the result!

Fozia

The Street Fighter Re: RanaRansher, Khan

I was by no means condoning the politicizing of cricket…simply stating the reality of a politically charged region where cricket was often the only means of expressing dissent.Mostly in a harmless manner like flag waving, drum beating etc and I think that is ok as long as people don’t get carried away with it and forget that they came to watch a cricket game.
I happen to like cricket, have played it for many years and watch it for the sheer fun of it. I am not immune to the extra intensity of Indo-Pak matches, but does that make me a bloodthirsty fan? Heck, no :-)

Re: RanaRansher…. “watching news clipping of Hindu - Muslim riots instead. May give you more satisfaction.”…..

Funny, you couldn’t express your disagreement without resorting to such remarks and *you * are advocating de-politicizing of cricket?

Fozia

The Street Fighter Ah Miandad! How can we ever forget him or Sharjah for that matter.

I am also reminded of the one-day match between India and the West Indies held in Srinagar....a packed stadium, West Indian flags flying everywhere and life-size posters of Miandad and Imran hanging from the chinars surrounding the stadium :-) Cricket was not just cricket in Kashmir. Rightly or wrongly, it was also a mode of political expression and Miandad`s performance was ever so often instrumental in providing a jubilant ring to the stifled voice of an entire generation.
And yes, Minadad will be showered with rose petals in Kashmir anytime.

Re:..and Mushtaq`s (expert commentator) scream, ``It`s a SSSIIIIIIIXXXXXX!!``.

Hmm...I always thought it was Iftikhar who said those words??

Fozia

Infinite in All Directions Re: Wasiq

So, infinities have not entirely been swept under the rug :)
Thanks for the preview. I will wait for part 2 before making any further comments.

Fozia

Infinite in All Directions I glanced at this article last week and realized that to do justice to it I had to read it over the weekend! I did, and I must say this is an extremely well written article. Wasiq, you have managed to impart the fundamentals in a remarkably lucid way.

Would it be possible for you to shed some more light on the process of Renormalization? The concept sounds interesting. My area of expertise is mathematics and as such Infinity is very much part of my `reality`....but how does a physicist go about conducting this separation of the infinite and the finite?

Looking forward to the next part.

Fozia

Christians of Pakistan A very thought provoking article.

I just want to point out that the janitor community in Kashmir, known as `vaatal` is also
discriminated against in the same way ( separate utensils etc ) even though they are fellow Muslims. Many of them have chosen different professions now but…it pains me to say…the stigma still remains.

Clearly, religious intolerance in not the only
reason for the mistreatment of Pakistani Christians. We , in South Asia, are still hung up on the caste system.