1 + 1 = 2 Expounded

Note—This is a piece I found in the book Science With A Smile, a collection of humorous scientific stories, anecdotes, and cartoons edited by Robert Weber.  Its authorship was attributed to Anon.

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

1 + 1 = 2      (1)

Anyone who has made a study of advanced mathematics is aware that 1 = ln e and 1 = sin^2 x  + cos^2 x.  Further

daum_equation_1463959708590

therefore Eq. (1) can be expressed more scientifically as

image002(2)

This may be further simplified by use of the relations

image003

and

image004.

Equation (2) may therefore be rewritten

image005(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 further expound Eq. (3); these are easily discovered once the reader grasps the underlying principles.

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