| Author | Message | ||
Maha Junior Artist Username: Maha Post Number: 2 Registered: 08-2008 Posted From: 70.156.210.150 Rating: N/A |
Thanks | ||
Basky_indya Side Hero Username: Basky_indya Post Number: 7510 Registered: 10-2007 Posted From: 65.30.78.134 Rating: N/A |
welcome maha. all india Utter Flop Hero Fans UUUUth President | ||
Maha Junior Artist Username: Maha Post Number: 1 Registered: 08-2008 Posted From: 70.156.210.150 Rating: N/A |
test | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 459 Registered: 06-2008 Posted From: 199.171.86.140 Rating: N/A |
Ok.......I will send it you.....give me ur mail ID....but may be 2morrow..its 12 here.... infact....if u have ever read Martin Gardner or 100 elementay problems of mathematics by Steinhaus.....they have this problem.. these class of problems are called pursuit problems...... | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 101 Registered: 05-2008 Posted From: 71.198.33.202 Rating: N/A |
babai..i want to know how u proved..can you pls explain me with diagram...ikkada kudarakapote ...send me a doc with little explanation ... | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 455 Registered: 06-2008 Posted From: 199.171.86.140 Rating: N/A |
coz speed is 1....nuvve ichavu "unit speed"...infact anything above 0.....will yield the same result..........that is exactly y its fractal...!!!!!!!!!!!!!!! | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 99 Registered: 05-2008 Posted From: 71.198.33.202 Rating: N/A |
first of all...dt time unite ni...length 1 lonunchi ela teestavu? | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 450 Registered: 06-2008 Posted From: 199.171.86.140 Rating: N/A |
I am super sure of it.........this is one of the proofs for constructing a log spiral with eccentricity 45 deg..... and the length in the limit n->inf that they each travel is l1..... I can bet anything on this........  | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 449 Registered: 06-2008 Posted From: 199.171.86.140 Rating: N/A |
say u start with a square of unit size...say an infinitesimal time dt elapses...now what you have is a shrinked square of side 1-dt and the sides rotated by 45 deg. Now what is this new squares side: assuming the first side is L1....it is Sqrt((L1-dt)^2+dt^2) with L1 =1...... i.e Sqrt(l1^2 + 2*dt^2 - 2*dt*l1) using dt->0 .......the above is Sqrt(l1^2- 2*dt*l1).... using the binomial identity (1+x)^(1/2) is (1+ (x/2)) iff mod(x) < 1 The above is l1*(1-dt).... Now recurse : l1 = 1 l2 = l1*( 1-dt) l3 = l2*(1-dt) ln = ln-1 *(1-dt) i.e ln = l1 *(1-dt)^n since l1 = 1 ln = (1-dt)^n.... for all dt !=0...this is a strictly decreasing function....and approaches 0 in lmit n->infinity So the side length goes to zero only after infinite iterations............... | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 87 Registered: 05-2008 Posted From: 71.198.33.202 Rating: N/A |
Qantum babai..1 unit time is correct anukunta....okasari check chesuko...or inko sari nee logic cheppu | ||
Basky_indya Side Hero Username: Basky_indya Post Number: 6071 Registered: 10-2007 Posted From: 65.30.78.134 Rating: N/A |
8 new IIT in India. comments plzzz all india Utter Flop Hero Fans UUUUth President | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 446 Registered: 06-2008 Posted From: 199.171.86.140 Rating: N/A |
This proof is wrong........it states they meet after 1 unit time............ | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 69 Registered: 05-2008 Posted From: 71.198.33.202 Rating: N/A |
ya ..i did just like just4fun babai cheppinattu,, Quant babai..oka sari inter lo IIT coaching class lu gurthu chesav... I have one more puzzle for you guys..I will post very soon... | ||
Hp1 Junior Artist Username: Hp1 Post Number: 99 Registered: 05-2008 Posted From: 203.17.68.1 Rating: N/A |
centre lo kalusthayani na uddhesham adhyaksha | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 445 Registered: 06-2008 Posted From: 99.141.75.30 Rating: N/A |
This was the question that they asked me when I interviewed at Goldman Sachs... | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 444 Registered: 06-2008 Posted From: 99.141.75.30 Rating: N/A |
easiest way is to recursively shrink ur square by dt and rotate it by 45deg...and keep ding it....u will see that corners of the shrunk squares will follow a Logarthmic spiral into the center of the center of the square....one needs to work out a geometric progression which eventually converge to 1 as n->inf... My recursive proof below is very stght fwd intuitively | ||
Kkd Side Hero Username: Kkd Post Number: 4787 Registered: 02-2008 Posted From: 68.196.116.154 Rating: N/A |
abbba chaa....  | ||
Just4fun Hero Username: Just4fun Post Number: 11261 Registered: 10-2007 Posted From: 24.131.221.241 Rating: N/A |
At any moment of time dogs will be at the corner of another square with smaller size and same center, size of square will decrease with time and finally they will meet at center. At any moment of time their speed toward center will be 1*cos(45) = 1/√2, and radial distance is √2, so they will meet after √2/ (1/√2) = 1 unit time and will travel unit distance. | ||
Mclovin Side Hero Username: Mclovin Post Number: 6753 Registered: 02-2008 Posted From: 24.0.13.16 Rating: N/A |
Asalu nenu kochhen wrong sadvinaa.. 4 corners lo oka dog, oka ant, two people unru ankunnaa.. lekunte eppudo cheppetonni.. apatki center la kalustaru ani cheppina... KKD: vaallu unde very small square lo.. lagethhi alasiponeeki neelaagaa 3miles lagettaru.. In this db, there's always someone watching you!!  | ||
Elcaminocapastrino Side Hero Username: Elcaminocapastrino Post Number: 4983 Registered: 03-2008 Posted From: 204.95.150.205 Rating: N/A |
babai....nuvvu ee company lo project manager em ledhu valla stocks kaana naa dhaggara untey ventaney ammesukunta | ||
Kkd Side Hero Username: Kkd Post Number: 4786 Registered: 02-2008 Posted From: 68.196.116.154 Rating: N/A |
lagethi lagethi evado okadu alisi aagipothadu thammudu...appudu andharu akkade meet avuthaaru....  | ||
Elcaminocapastrino Side Hero Username: Elcaminocapastrino Post Number: 4982 Registered: 03-2008 Posted From: 204.95.150.205 Rating: N/A |
okkasari GOOD WILL HUNTING lo Matt damon ni choopichav babai...good one | ||
Razesh Hero Username: Razesh Post Number: 12088 Registered: 12-2006 Posted From: 202.153.41.36 Rating: N/A |
Center lo meet avuthaayi... | ||
Hp1 Junior Artist Username: Hp1 Post Number: 96 Registered: 05-2008 Posted From: 203.17.68.1 Rating: N/A |
nenu ippude thinking start chesa | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 443 Registered: 06-2008 Posted From: 99.141.75.30 Rating: N/A |
"they run infinite steps.......but cover a finite distance"......this is the beauty of fractal calculus..........One needs to have a sound understanding of measure theory to appreciate this stuff......... In fact this is a koch fractal of type 1 ...if I am not wrong | ||
Quantummorphed Junior Artist Username: Quantummorphed Post Number: 442 Registered: 06-2008 Posted From: 99.141.75.30 Rating: |
They will eventually meet at the geometric centre of the square after infinite (large number) of steps after they a follow a logarthmic spiral....there is a 4 way symmetry to this problem.... Use recursion to understand this and some infinitesimal calculus....assume that after the first run in an infinitesimal run...the square is now smaller with side length ~~ 1-dt where dt is the contraction in infinitesimal time dt(speed is 1)...recursively after "n" steps.....your squares length is (1-dt)^n. The number inside is between 0 and and will reach close to 0 as n->infinity.. They will def meet....... This is a "pursuit problem".........similar types exist for a triangle...any one who might have studied JEE physics will identify this immediately.... It is also called the fractal Zena's paradox..... The path they follow is a 45deg log spiral and on an avg all the dogs travel 1 mt.. | ||
Kadapanagfan Side Hero Username: Kadapanagfan Post Number: 4252 Registered: 12-2006 Posted From: 13.8.137.11 Rating: N/A |
square antey all side equal kabattiu and they are running with unit spped kabatti asalau kalavaru kadha........... | ||
Spy_india Comedian Username: Spy_india Post Number: 1566 Registered: 02-2008 Posted From: 170.35.224.64 Rating: N/A |
anni same speed lo oek direction lo potunte okatini okati ekkada meet avutaay ?? | ||
Mclovin Side Hero Username: Mclovin Post Number: 6746 Registered: 02-2008 Posted From: 24.0.13.16 Rating: N/A |
center lo kalustaaraa? In this db, there's always someone watching you!! | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 68 Registered: 05-2008 Posted From: 159.145.7.90 Rating: N/A |
I don't know but ninna naa friend okadu mail chesadu... | ||
Spy_india Comedian Username: Spy_india Post Number: 1565 Registered: 02-2008 Posted From: 170.35.224.64 Rating: N/A |
msft questions aa ahaa ! vaalla interview lo ilaane adugutaaru questions | ||
Swayamkrushi Junior Artist Username: Swayamkrushi Post Number: 67 Registered: 05-2008 Posted From: 159.145.7.90 Rating: N/A |
There are four dogs/ants/people at four corners of a square of unit distance. At the same instant all of them start running with unit speed towards the person on their clockwise direction and will always run towards that target. How long does it take for them to meet and where? babai lu ...meeku evarikina telisthe cheppandi...try before googling ..it will be fun solving (atleast to me)...naaku kaasepu juttu peekkunte vhachindi.... answer kanipedithe ..please explain... |
