64 = 65?

[Carte Blanche]

Can anyone explain this? I'm confused

[Zunaid]

64 = 65 for sufficiently large values of 64

This is a nice example of geometric illussion. The two triangles are not only not congruent they are not equal.

In real life the final picture would actually have some gaps if the trinagles were equal - as it is it's a very subtle 4 sided geomteric object.

Looking at it another way,

The tan of the smallets angle of the triangle is 3/8, in the tweaked picture it is 5/13 (ie not the same triangle)

[Zunaid]

Did a google hunt to see if there is a pictorial explanation of my explanation.

Here it is:

http://neurobashing.com/monkey/archives/001356.html

[Ehsan]

Just when I saw that post the first name that came on my mind who will answer that was Dr. Zunaid and there you go!

[Rubu]

how about his one? the same kinda thing.

[Zunaid]

AgentSmith,

It is not poilte to publish moderator's pictures without their permission

Note the chopped off head on the left

[Rubu]

Mathmetical explanation of 64=65

This unique piece of math work was done by a friend of mine (a group work actually, took us about 4-5 class periods, but was more exciting than listening to the teacher . ) anyway, this mathmetically explain why 64=65. just add 60 on both side of the equation at the last.

u'll have a better understanding of what it means by "jaha bahanno, taha tepanno".



tell me whats wrong? I know the answer, but have some fun with it before i tell u.

[fab]

Originally posted by Zunaid
Note the chopped off head on the left

And that would be you?

This unique piece of math work was done by a friend of mine (a group work actually, took us about 4-5 class periods, but was more exciting than listening to the teacher)

It took you 4-5 class periods to make up the joke, or 4-5 class periods to solve it?

The basic problem is that the sqrt of a number can be +ve or -ve i.e sqrt(4) = +/-2. The fourth last line simplifies to (-0.5)^2 = (0.5)^2 and so the third last line should read +/-(sqrt(4-9/2)) = +/-(sqrt(5-9/2))
Second last line should be -(4-9/2) = (5-9/2)
And so last line should be -4+9/2 = 5-9/2

[Rubu]

fab, why are u calling it a joke? yea, we created it, actually it got created by us. without knowing why. i mean did not know the reason the answer comes out like that (we were in 8th grade at that time).

.......in simple word, we decide to pick the invalid result of a 2nd order equation. it did give us quite a few fun, since the teacher as well did not know why is this happening.

[fab]

Originally posted by AgentSmith
fab, why are u calling it a joke? yea, we created it, actually it got created by us. without knowing why. i mean did not know the reason the answer comes out like that (we were in 8th grade at that time).

Okay.. 'puzzle' if you wish to call it that. I didn't mean 'joke' as an insult. It's pretty good to come up with a 'puzzle' like that when you are only 12 years old cheers

[rafiq]

My son just started 8th grade last week. What can I do to make him put down his damn Che autobiography (it's a thick book, and never seems to end) and create some math puzzles? In fact, I am going to give him the above puzzle and if he can't solve it I am going to beat him silly.

[chinaman]

And it will all be AgentSmith's fault

[Nasif]

Here is the trick in detail..... :P

---

If a=c and b ≠ 0 then,

(a-b)² = (c-b)²

a² – 2ab + b² = c² – 2bc + b²

a² – 2ab = c² – 2bc

a (a-2b) = c (c – 2b)

 

As, a = c,    (Given)

Therefore, -a ≠ (c – 2b)

 

But if we create an incorrect equation:

-a = (c – 2b) ................. (i)

 

Then we create false equality every time for any given a and c.

Given, -a = (c – 2b), note the following:

a² - 2ab

= [-(c – 2b)]² - 2[-(c-2b)]b [substitution using (i)]

= c² – 4bc + 4b² + 2bc - 4b² .......... [Note 1]

= c² – 2bc

 

Therefore,

a² - 2ab = c² – 2bc  ............... (ii)

 

Now we can always prove a = c

Let, a = 7 and c = 11 (randomly chosen value for a and c, anything will work).

 

-a = (c – 2b)

-7 = 11 – 2b

b = (11 + 7) / 2

b = 9    .................. (iii)

 

Find value of:

c² – 2bc

= (11)² – 2·9·11

= 121 – 198

= -77

 

Now create equation (our a=7, b=9 and c=11):

-77 = -77

c² – 2cb = c² – 2cb

a² – 2ab = c² – 2cb [see equation (ii)]

a² - 2ab + b² = c² – 2cb + b²

7² - 2·7·9 + (9)² = 11² – 2·11·9 + 9²  

(7 – 9)² = (11 – 9)²

√ [(7 – 9)²] = √ [(11 – 9)²]

(7 – 9) = (11 – 9)

7 = 11

 

The proof is incorrect as you guys already explained the trick. We killed the -ve sign (see Note 1, line in red). We killed it by squaring. This created the incorrect equation a² - 2ab = c² – 2bc. Which in turn results in incorrect result of 7=11.

Using this method you can prove any two numbers equal!

Lets prove 6 = 14 (You have to do all the work above before-hand to show your trick!)

-84 = -84

36 - 120 = 196 - 280

6² - 2·6·10 + 10² = 14² - 2·14·10 + 10²

(6 - 10)² = (14-10)²

√ [(6 - 10)²] = √ [(14-10)²]

(6 - 10) = (14 - 10)

6 = 14 (!)

---

Killed yet another hour of life chasing nothing

Edited on, September 6, 2004, 9:12 AM GMT, by nasif.
Reason: Typo

[Rubu]

Originally posted by chinaman
And it will all be AgentSmith's fault

thats fine.

[FaltuRidwanBhai]

khaise amare...........cricket theke dekhi akdom pura algebray dhuke porlam. aita mone hoi wrong number a gese.

[Unknown]

6 4 = 6 5
a b = b a

let = a = 1 = b
a.b = b.a

a.b = 6x6 = 36
a.a = 6x5 = 30
a = a.b - a² = 36 - 30 = 6

b.b = 4x6 = 24
b.a = 4x5 = 20
b = b.b - b.a = 4


a(+)b = 6(+)4 = 64

b.a = 6x6 = 36
a.a = 6x5 = 30
a = b.a - a² = 36 - 30 = 6

a.a = 5x5 = 25
a.b = 5x4 = 20
a= a² - a.b = 25 - 20 = 5

a(+)b = 6(+)5 = 65

since a b = b a
64 = 65 :P

I hope that was not a difficult concept to grasp

Edited on, September 6, 2004, 8:12 PM GMT, by Unknown.

[Unknown]

Source: http://nasa.perbang.dk/perbang.com.cms?aid=161


About the formula (in the previous post), its called the addition of numerical instances... I came up with that myself


Edited on, September 6, 2004, 9:20 PM GMT, by Unknown.
Reason: some information was not relevant

[Mueid]

mago re!!..wat r u guys?!

[Zunaid]

Originally posted by rafiq
My son just started 8th grade last week. What can I do to make him put down his damn Che autobiography (it's a thick book, and never seems to end) and create some math puzzles? In fact, I am going to give him the above puzzle and if he can't solve it I am going to beat him silly.

Rafiq, don't stifle the kid! We desis are producing way too many engineers and doctors - namby pamby one's who vote republikan as soon as the money starts puring in. We need a few more of the active types out here..

[nishy]

did my picture made the answer clear?