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Mallik
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Username: Mallik

Post Number: 5209
Registered: 10-2008
Posted From: 162.116.29.69

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Posted on Thursday, May 21, 2009 - 06:30 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Anand_n:

Each piece of cake now has a net volume of X/2 - Y/2 which is equal to (X-Y)/2 as desired.


Locus method elaa untadi ante..

Each cuboid/cube(i can cut the piece such that its a cube), has three dimension each: x1, y1, z1:: x2, y2, z2 and thei smaller piece center move each time I cut the piece in a different location. Meeru cheppina volumes ni equate cheshi, locus equation kanukkoni solve cheyyaali ani naalo unna ramanujam thinking.. :D
In this db, there's always someone watching you!!
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Mallik
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Username: Mallik

Post Number: 5206
Registered: 10-2008
Posted From: 162.116.29.69

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Posted on Thursday, May 21, 2009 - 05:34 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

Andy garu: I need to think on Locus. Inter 2nd lo Cutting circles ani sesinam kadaa.. affud locus ni use sesevaallam..

Lines ante naaku maa frnd gaadi joke gurthochhindi.. Eng 1st year lo graphics ante maavodiki shake.. oka saari assignment chestunte.. orei.. aa two points ni join cheyyi bey ante.. mama.. distance entha mama ani adigindu.. appudu maa lukku..


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Anand_n
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Username: Anand_n

Post Number: 4107
Registered: 02-2008
Posted From: 68.206.110.236

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Posted on Thursday, May 21, 2009 - 05:27 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Anand_n:

A straight line L1 thru centre of Cake makes it into 2 pieces with volume X/2
A straight line L2 thru centre of Hole makes it into 2 holes with volume Y/2

If L1 = L2




Chaa -2 D lo alochinchi 3 D lo raaste ilage untundi...


Make that a Plane not Line - Plane P1 and P2 passing thru the centrepoint of the cuboids...(P1 =P2)


Line works for 2D rectangles...
aa chal ke tujhe main leke chalu ik aise gagan ke tale
jahan gam bhi na ho, aansoo bhi na ho,bas pyaar hi pyaar pale
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Mvssr75
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Username: Mvssr75

Post Number: 635
Registered: 05-2008
Posted From: 12.10.219.164

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Posted on Thursday, May 21, 2009 - 04:52 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Anand_n:




Thank you. Got it :-)
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Anand_n
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Username: Anand_n

Post Number: 4105
Registered: 02-2008
Posted From: 68.206.110.236

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Posted on Thursday, May 21, 2009 - 04:51 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Mvssr75:

L1 need not be eaul to L2 to make them equal.




Ardham kaledu - are you talking about the "length of the line" as in line segment ? I am using the geometric definition of a Line - infinite length :-)
aa chal ke tujhe main leke chalu ik aise gagan ke tale
jahan gam bhi na ho, aansoo bhi na ho,bas pyaar hi pyaar pale
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Mvssr75
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Username: Mvssr75

Post Number: 634
Registered: 05-2008
Posted From: 12.10.219.164

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Posted on Thursday, May 21, 2009 - 04:49 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

Question :

You are right but a question.

L1 need not be eaul to L2 to make them equal. why did you assume that ?
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Anand_n
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Username: Anand_n

Post Number: 4101
Registered: 02-2008
Posted From: 68.206.110.236

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Posted on Thursday, May 21, 2009 - 04:19 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Mallik:

You can prove this mathematically by using 'Locus' method anukuntunnaa..




Mathematical representation of the solution I gave below...

Cake volume - X
Hole volume - Y

Problem : Make 2 pieces with volume (X-Y)/2

A straight line L1 thru centre of Cake makes it into 2 pieces with volume X/2
A straight line L2 thru centre of Hole makes it into 2 holes with volume Y/2

If L1 = L2

Each piece of cake now has a net volume of X/2 - Y/2 which is equal to (X-Y)/2 as desired.

What is the Locus method proof ? :-)
aa chal ke tujhe main leke chalu ik aise gagan ke tale
jahan gam bhi na ho, aansoo bhi na ho,bas pyaar hi pyaar pale
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Mallik
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Username: Mallik

Post Number: 5198
Registered: 10-2008
Posted From: 162.116.29.69

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Posted on Thursday, May 21, 2009 - 03:37 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

Trans: You can prove this mathematically by using 'Locus' method anukuntunnaa..
In this db, there's always someone watching you!!
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Anand_n
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Username: Anand_n

Post Number: 4100
Registered: 02-2008
Posted From: 68.206.110.236

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Posted on Thursday, May 21, 2009 - 03:25 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Transcendental:

nenu yevovo calculations vestunnanu ..




:-)ilantivatiki formulas kanna visuals work better
aa chal ke tujhe main leke chalu ik aise gagan ke tale
jahan gam bhi na ho, aansoo bhi na ho,bas pyaar hi pyaar pale
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Eluri_kurradu
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Username: Eluri_kurradu

Post Number: 5265
Registered: 02-2008
Posted From: 159.182.1.4

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Posted on Thursday, May 21, 2009 - 03:24 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Risingstar:

(a+b)2=a2+b2+2ab


Tappu
(A+B)* 2 = 2A + 2B
Ekkado munigi ikkada tela
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Transcendental
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Username: Transcendental

Post Number: 2420
Registered: 10-2008
Posted From: 128.221.197.55

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Posted on Thursday, May 21, 2009 - 03:20 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)


Anand_n:

Very simple kada..

A line through the centre of a rectangle bisects it...

So when you join the the centres of the two rectangles you bisect both of them...

The whole is halved and the the part removed is halved as well, as a result the balance cake is halved.




hmm ..ippudu veligindi .. nenu yevovo calculations vestunnanu ..Thnaks ji.
_Trans _
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Risingstar
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Username: Risingstar

Post Number: 8391
Registered: 08-2008
Posted From: 67.132.206.254

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Posted on Thursday, May 21, 2009 - 03:16 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

(a+b)2=a2+b2+2ab
Now everybody will use Colour Paper & Colour TV in Toilet
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Anand_n
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Username: Anand_n

Post Number: 4099
Registered: 02-2008
Posted From: 68.206.110.236

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Posted on Thursday, May 21, 2009 - 03:15 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

Very simple kada..

A line through the centre of a rectangle bisects it...

So when you join the the centres of the two rectangles you bisect both of them...

The whole is halved and the the part removed is halved as well, as a result the balance cake is halved.
aa chal ke tujhe main leke chalu ik aise gagan ke tale
jahan gam bhi na ho, aansoo bhi na ho,bas pyaar hi pyaar pale
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Transcendental
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Username: Transcendental

Post Number: 2419
Registered: 10-2008
Posted From: 128.221.197.55

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Posted on Thursday, May 21, 2009 - 03:10 pm:   Insert Quote Edit PostDelete PostPrint Post   Move Post (Moderator/Admin Only)Ban Poster IP (Moderator/Admin only)

Maths paranga yela proof cheyyalo cheppandi konchem .. naa burra sarigga panichheyyad ledu

Q. Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?

ANS. Join the centers of the original and the removed rectangle. It works for cuboids too! BTW, I have been getting many questions asking why a horizontal slice across the middle will not do. Please note the "any size or orientation" in the question! Don't get boxed in by the way you cut your birthday cake :-) Think out of the box.
_Trans _

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