Are you a Ramanujan?
Posted 12th November 2011 at 12:58 AM by Dr. L. Ramakrishnan
I am not a mathematician. Reading a book on Ramanujan, the great mathematician of the 20th Century, even I have been motivated to brush up my algebra. Whether you are a mathematician or not the book: "The man who knew infinity: A life of the Genius Ramanujan" by Robert Kanigel (first published in 1991) will perhaps interest you for its simple explanations on various mathematical principles. I was thrilled (being a non-mathematician) with this simple algebraic puzzle which proves 2 = 1 that the author describes to demonstrate how "Proof" is important for any theorem. .:
Let
a = b
multiply both sides by a
a2=ab
add (a2-2ab) to both the sides
a2 + (a2-2ab) = ab +(a2-2ab)
simplify
2a2 – 2 ab = a2 – ab
rearrange
2 (a2 – ab) = 1 (a2 – ab)
2 (a2 – ab)/ (a2 – ab) = 1
2 = 1
Obviously 2 is NOT equal to 1. Where is the catch ?
To me it is interesting because many times we stumble upon impossibles and wonder how we arrived at such impossibles. If only we have a thorough understanding of the subject matter we will not; our ignorance probably puts us at a disadvantage when we come across such absurd results.
If we are all Ramanujans probably most of us will find out the fallacy in the argument or in our decision making process. As lower mortals many continue to believe the possibility of the impossible.
Let
a = b
multiply both sides by a
a2=ab
add (a2-2ab) to both the sides
a2 + (a2-2ab) = ab +(a2-2ab)
simplify
2a2 – 2 ab = a2 – ab
rearrange
2 (a2 – ab) = 1 (a2 – ab)
2 (a2 – ab)/ (a2 – ab) = 1
2 = 1
Obviously 2 is NOT equal to 1. Where is the catch ?
To me it is interesting because many times we stumble upon impossibles and wonder how we arrived at such impossibles. If only we have a thorough understanding of the subject matter we will not; our ignorance probably puts us at a disadvantage when we come across such absurd results.
If we are all Ramanujans probably most of us will find out the fallacy in the argument or in our decision making process. As lower mortals many continue to believe the possibility of the impossible.
Total Comments 4
Comments
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Interesting. I am not a mathematician either, but I have a lot of respect for those who are really into math. I mean - I love numbers, but the "advanced" and theoretical stuff gets me. I made it through a year of calculus way back in my college days (1970's), but I was a "C" student.Posted 13th November 2011 at 06:06 PM by Marc 
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I asked Tracey to ask her son about this one. Here's his response:
Hey Marc,
My mom showed me the math problem you sent, so here are my comments. First, I'll re-list and number each step.
(1) Let a=b.
(2) a^2 = a*b
(3) a^2 +a^2 - 2a*b = a*b + a^2 - 2a*b
(4) 2a^2 - 2a*b = a^2 - 2a*b
(5) 2*(a^2 - a*b) = 1*(a^2 - a*b)
(6) 2*(a^2 - a*b)/(a^2 - a*b) = 1
(7) 2 = 1
Ok, so the problem arises in step (6). Since it was assumed in step (1) that a=b, upon substitution the quantity
a^2 - a*b equals b^2 - b*b = b^2 - b^2 = 0. So in step (6), division by 0 is occurring, which is a big no-no.Posted 14th November 2011 at 06:15 PM by Marc
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Are you a Ramanujan ?
Absolutely Right ! Genius in the making !!Posted 14th November 2011 at 11:22 PM by Dr. L. Ramakrishnan 
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Ramanujan,a rare genious.Apart from his maths his humble, impoverished life brings tears into your eyes.I have seen his his younger brother in CHENNAI some 50 years back.
-SitapatyPosted 8th January 2012 at 02:26 AM by sitapaty
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