A funny derivation

March 19, 2008 — Karthik

Every new scientist must learn early that it is never good taste to designate the sum of two quantities in the form:

1 + 1 = 2 \qquad (1)

Anyone who has made a study of advanced mathematics is aware that:

1 = \mathop{ln} e

1 = \sin^2 x + \cos^2 x

2 = \sum_0^\infty \frac{1}{2^n}

Therefore eq. (1) can be expressed more scientifically as:

\mathop{ln} e + \sin^2 x + \cos^2x = \sum_0^\infty \frac{1}{2^n} \qquad (2)

This may be further simplified by use of the relations:

1 = \cosh y \sqrt{1 - \tanh^2 y}

e = \lim_{z->\infty} ( 1+\frac{1}{z} )^z

Equation (2) may therefore be rewritten as:

\mathop{ln}{\lim_{z->\infty} \left(1+\frac{1}{z}\right)^z} + sin^2 x + cos^2 x = \sum_0^\infty \frac{\cosh y \sqrt{1 - \tanh^2 y}}{2^n} \qquad (3)

At this point it should be obvious that eq. (3) is much clearer and more easily understood than eq. (1). Other methods of a similar nature could be used to clarify eq. (1), but these are easily divined once the reader grasps the underlying principles.

Posted in General, Humour. 8 Comments »

8 Responses to “A funny derivation”

  1. markc86 Says:
    June 4, 2008 at 11:45 pm

    This was re-published in the anthology “Science with a Smile”, although since I do not have the book right now, I do not know the original journal it was published in.

    Where did you find it?

  2. Karthik Says:
    June 5, 2008 at 2:27 am

    Oops, I should have credited that. I got it from:
    http://buddy.bbsg.ca/jokes/mathjokes.php

    There a lot many more hilarious math jokes on the site!

  3. rohedi Says:
    December 26, 2008 at 1:19 am

    he he he, I believe the discussion about 1+1=2 is not the ordinary math joke. Because recently is also discussed intensively in MIT. But, my proof for the 1+1=2 more easily as appear at this address :
    http://castingoutnines.wordpress.com/2008/12/10/leibniz-on-112/
    Please visit to the website.

  4. Denaya Lesa Says:
    January 9, 2009 at 9:42 am

    I am interested to Nadya’s statement On castingoutnines.wordpress.com/2008/12/10/leibniz-on-112/
    “Sorry sir, my simple question is not a joke. it will reveal the secret of science that maybe next time to becomes our living be better. But if we ask to the mathematicians about 1-1 =0, I am sure they will answer with the relaxed that 1 + (-1) = 0. Thinking about my purpose sir. Thx.” How about you all if somebody asks how to get 1-1 ?.

  5. Denaya Lesa Says:
    January 9, 2009 at 10:17 am

    apologize rohedi, I’ve copied your comment at this address
    http://math152.wordpress.com/2008/10/08/leonhard-euler/#comment-215

  6. Denaya Lesa Says:
    January 12, 2009 at 5:47 pm

    Well, now I will give a challenge for you all.
    Please prove the trigonometric indentity

    [sin(x)]^2+[cos(x)]^2=1

    using three different’s way.

  7. Denaya Lesa Says:
    January 12, 2009 at 5:55 pm

    Hi aria (http://ariaturns.wordpress.com), you may also appreciate for the above challenge.

  8. Denaya Lesa Says:
    January 12, 2009 at 6:05 pm

    Hi zaki (http://zaki.math.web.id/) you may go with me to USA if you can show me how to get 3^(1/3) without using calculator and numerical method. Okay, are you ready? please post your answer at this funny blog.


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