Search found 194 matches

by SK Mody
23 Sep 2008 22:43
Forum: Technology & Economic Forum
Topic: Global Economy
Replies: 2337
Views: 444311

Re: GLOBAL ECONOMY

India should re-joice at the decline of US institutions-- http://www.dnaindia.com/report.asp?newsid=1192432 rvaidya Quoting from the article: ... What should India have done? Immediately after the collapse of Freddie Mac and Fannie Mae and the crisis in many investment banks, our finance ministry s...
by SK Mody
18 Sep 2008 21:32
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Hmm. Yes. Sloppy thinking on my part. Thanks.
by SK Mody
17 Sep 2008 19:49
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

I have a logic problem. Logic is a lot like mathematics. So, I think this thread would be an appropriate thread for this problem. I friend of mine shared this problem with me over masala dosha dinner. Nothing unethical involved here so please take it easy. Problem: We have 25 horses arranged as fol...
by SK Mody
14 Sep 2008 12:53
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

I don't know if this is a "well known" problem, but it's something that occurred to me. A car is parked facing west on the side of the road, and parallel to it. It needs to make an N-point turn and go east. Given that the turning radius of the car is 'r' and the width of the road is 'w': (...
by SK Mody
09 Sep 2008 22:05
Forum: History & Current Affairs Archive
Topic: Caucasus Crisis
Replies: 1226
Views: 97855

Re: Caucasus Crisis

It seems like Putin's Russia is slowly giving up to the pressure from the west, after a month long rheotric and heorisms.... Medvedev: Russia to Pull Forces from Georgian Buffer Zone http://voanews.com/english/2008-09-08-voa22.cfm Russia Will Pull Back Peacekeepers After Medvedev-Sarkozy Talks http...
by SK Mody
07 Sep 2008 02:17
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

The number of paths in nxn grid, between two diagonal points, if you can't cross the diagonal line is given by the same formula. [Catalans formula] Yes - one can think of an open bracket as +1 and close bracket as -1. Every x_i in x_1/x_2/.../x_n is associated with exactly one bracket (If the brack...
by SK Mody
06 Sep 2008 16:23
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

How many different ways are there to evaluate the fraction: v/w/x/y/z Or equivalently how many different ways are there to evaluate v-w-x-y-z Can you generalize your answer to: x1/x2/x3/ ... /x_n ? Assuming that value depends on where one puts "(" ... Don't peek unless you want to (2n-2)!...
by SK Mody
04 Sep 2008 08:25
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

How many different ways are there to evaluate the fraction:
v/w/x/y/z
Or equivalently how many different ways are there to evaluate
v-w-x-y-z

Can you generalize your answer to:
x1/x2/x3/ ... /x_n
?
by SK Mody
02 Sep 2008 21:34
Forum: Technology & Economic Forum
Topic: Global Economy
Replies: 2337
Views: 444311

Re: GLOBAL ECONOMY

Thanks for the laughs evryone. Previous conversation was hilarious. :lol:
by SK Mody
29 Aug 2008 01:01
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Ah yes, forgot about the zeros. Can't do without them. :)
by SK Mody
28 Aug 2008 23:42
Forum: Technology & Economic Forum
Topic: Indian Autos Thread
Replies: 3784
Views: 413920

Re: Indian Autos Thread

Why are TATA's wasting their time with WB govt? Are they trying to live up to their "socially responsible" image or to get on the good side of UPA govt? They should cut their losses and move to another state or they will get taken for a long ride.
by SK Mody
28 Aug 2008 21:44
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

You can, perhaps simplify it a little, just take two numbers with the same 'r' - as you proceeded to do, and subtract. the closest two .. that you will get 999... followed by 0's . Certainly makes it a lot shorter. By the way, using the same idea, it is not difficult to show that given any two digi...
by SK Mody
28 Aug 2008 04:09
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Amber G. wrote:Rumor is that a new "largest known prime" (mersenne prime number) number is found..


It would be interesting to know if this has any implications for cryptography.
by SK Mody
28 Aug 2008 03:40
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Amber G, here is my solution to your ankan problem (actually a slightly stronger result): I will show that given any p, there is a multiple of p that has only 0's and 1's. Let p be any number. The remainder when 10^k (k = 0, 1, 2, ... etc ) is divided by p is some number between 0 and p-1 inclusive....
by SK Mody
20 Aug 2008 20:39
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

sugriva wrote:
The only way a vertex of a sub-triangle will have a label at all is if it lies on one of the original edges AB, BC, CA.



This need not be the case. There can be any number of interior triangles.
See this picture
by SK Mody
19 Aug 2008 20:09
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

A number of men and women stand in a line holding hands. There are an unspecified number of men and women, the only condition being that the there is a woman at the beginning of the line and a man at the end. If two members of the opposite sex hold hands, they are obliged to have a baby :mrgreen: ....
by SK Mody
18 Aug 2008 23:20
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

A number of men and women stand in a line holding hands. There are an unspecified number of men and women, the only condition being that the there is a woman at the beginning of the line and a man at the end. If two members of the opposite sex hold hands, they are obliged to have a baby :mrgreen: . ...
by SK Mody
18 Aug 2008 23:07
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Any two closed curves in space can be moved into exactly one of the following standard positions. This determines the linking number. Each curve may pass through itself during this motion, but the two curves must remain separated throughout. Not noticing the bolded part could lead to confusion :) .
by SK Mody
18 Aug 2008 22:11
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

What I said is this: There is a configuration of TWO and just two entangled loops that have zero linking number. If the linking number is the circulation of the magnetic field around the loop, and the linking number is zero, the net current through the loop is zero. How is that possible for only tw...
by SK Mody
18 Aug 2008 20:29
Forum: Technology & Economic Forum
Topic: Indian Autos Thread
Replies: 3784
Views: 413920

Re: Indian Autos Thread

Interesting update in auto tech. GM's plug in hybrid called the volt. Goes 40 miles just on battery and can be recharged by plugging a cord into a household outlet! Should be due out in 2010. Of course Toyota should also have a plug in hybrid then. http://www.nytimes.com/2008/08/15/business/15volt....
by SK Mody
18 Aug 2008 14:08
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Also there may be another problem with your code. Even assuming that your curves are actually polygons defined by the vertices at the nodes, I'm not sure of the accuracy of the calculation. If two nodes are spaced far apart, you may need to split that straight line segment into a further set of node...
by SK Mody
18 Aug 2008 13:58
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

[dr(1_k) x dr(1_m)]


Don't know if you actually mistyped it here or in the actual program. [dr(1_k) x dr(2_m)].
by SK Mody
18 Aug 2008 01:54
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

So pretend one closed loop is carrying a unit current. Write down by Biot-Savart the magnetic field generated by this current. Now compute the circulation around the second loop of this magnetic field and apply Ampere's law. Immediately you will get the formula of the linking number as on the Wiki ...
by SK Mody
15 Aug 2008 23:06
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Here is a math question I have been trying to solve for a particular problem perhaps a guru here can shed some light. How can I find out if 2 closed paths in a 3-Dimensional space are entangled? Are there any mathematical formulation that will give an boolean answer (True/False) for 2 closed paths....
by SK Mody
13 Aug 2008 23:12
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Hope that vsunder will be back. It will take some of us from being freshers to post grads.
by SK Mody
13 Aug 2008 22:58
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Good Sol.

Those who are interested check out RM>AM>GM>HM. It is a good exercise to prove.
Also take a look at this Mean page on wiki.
by SK Mody
13 Aug 2008 10:30
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

another easier solution to; Show that ( 1/a - 1 ) * ( 1/b - 1 ) * ( 1/c - 1 ) is equal to or greater then 8. (1/a - 1)(1/b - 1)(1/c - 1) = (1 - a)(1 - b)(1 - c)/abc = (b + c)(a + c)(a + b)/abc Now a - 2sqrt(a)sqrt(b) + b = ( sqrt(a) - sqrt(b) )^2 >= 0 Therefore a + b >= 2sqrt(a)sqrt(b) Same for (a +...
by SK Mody
13 Aug 2008 10:21
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Bear with me as math is not my strong point. I may be talking nonsense here but I'm gonna school you guys on what i think is the solution : Number of ways of picking 2 out of 3 candies being the same for a single item in the set : C(3,2) = 3! / 2!(3-2)! C(3,2) = 3 Total number of ways of picking 2 ...
by SK Mody
13 Aug 2008 02:14
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Yup, it is.
by SK Mody
13 Aug 2008 01:12
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

There is a box containing lots of milk chocolates, coconut toffees and bittersweets (there may be different quantities of each). I choose 3 with eyes closed. Show that the probability that I will get at least two of one type is greater than or equal to 7/9. (Assume that there are enough sweets in th...
by SK Mody
13 Aug 2008 00:33
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

a, b, c are positive and a + b + c = 1 Show that ( 1/a - 1 ) * ( 1/b - 1 ) * ( 1/c - 1 ) is equal to or greater then 8. Given that a+b+c = 1 The minimum value of 1/a + 1/b + 1/c is when a = b = c = 1/3. (This can be shown by first noting that the minimum in such a case must be a local turning point...
by SK Mody
11 Aug 2008 19:06
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Amber G wrote: There is a carpet 9(units) x 16 (units), and you want to cover 12 x 12 square. In how many (minimum) pieces you have to cut the original carpet (and resew them) to make it fit 12 x 12.? Solution 1: Two Pieces. Use a staircase cut. Start 4 units down from top left and cut 3 units right...
by SK Mody
11 Aug 2008 03:18
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

I would like make a request to members. To problem posters: Please give sufficient time for solution. I think even if a person visits the thread every other day, he should have a chance to have a go at some of the problems. I suggest the following time limits. Problems considered easy: at least 3 da...
by SK Mody
11 Aug 2008 03:05
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Here is the first lemma: Take a square it works for a cube in any dimension. Now play the following game. Lets take a square for example. Bisect each side you get now 4 congruent mini squares. Call this Step 1. Each congruent mini square can be bisected further to get now 16 mini squares in step 2....
by SK Mody
02 Aug 2008 22:16
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

There are also other possibilities that you can consider 4n-5n=380 = (1*2*10*19) First solve 4n-5m=1 n=9, m=7 is a solution. Therefore 380*9 = 3420, 380*7 = 2660 is a solution. We can for example also solve 4n-5m=2 and then multiply the solution by 180. and so on ... But all these solutions are rel...
by SK Mody
02 Aug 2008 21:58
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Two Not so Hard Problems: 1. (Old problem from Hindu Math sources) A dairy farm has exactly 75% cows, and the rest 25% are buffaloes. Also exactly 80% of all these animals are producing milk (rest 20% are non-milk producing). There are exactly 76 milk producing cows in the farm. What is the total n...
by SK Mody
30 Jul 2008 23:42
Forum: Terrorism Archive
Topic: Blasts in Ahmedabad
Replies: 743
Views: 54563

Re: Blasts in Ahmedabad

Don't know if this has been posted before, from nightwatch India: At least two persons died and six were injured when eight explosions triggered by a timer device detonated in Bangalore’s central business district and other areas housing the headquarters of international information technology (IT) ...
by SK Mody
28 Jul 2008 12:48
Forum: Technology & Economic Forum
Topic: BR Maths Corner-1
Replies: 1817
Views: 120536

Re: BR Maths Corner-1

Yes, I see. My changing the reference frame to the rotating one already assumed that the ball had only radial velocity in the rotating frame. Sorry, I have not read/understood the whole post, so you already know that, but, radial velocity will experience the other (Coriolis) force. This will actual...

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