Brilliant integral calculation

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Discussion Overview

The discussion revolves around the use of mathematical notation in integral calculations, with participants sharing their perspectives on clarity and complexity in mathematical expressions. The scope includes conceptual clarification and a debate on notation practices in mathematics.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants express concern that mathematical notation can become overly complicated, suggesting that it may detract from understanding.
  • Others argue that the notation in question is standard and appropriate, emphasizing that it is common for mathematicians to relate simpler problems to more complex ones.
  • A participant questions what is considered excessive in the notation, specifically referencing the use of parentheses around certain terms.
  • Another participant defends the complexity of the notation, suggesting that it can lead to more interesting arguments and proofs, citing an example related to the infinitude of prime numbers.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the notation is excessive or appropriate, indicating a disagreement on the clarity and necessity of complexity in mathematical expressions.

Contextual Notes

Some assumptions about what constitutes excessive notation may vary among participants, and the discussion does not resolve these differing perspectives.

Office_Shredder
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I just saw this and thought that sometimes people can get a bit too carried away with their mathematical notation. Hope you enjoy!

http://img695.imageshack.us/img695/9690/weirdintegralcalculatio.jpg
 
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But that's the standard way that "real mathematicians" solve easy problems: show the problem is equivalent to a harder problem that has been solved already. :smile:
 
Office_Shredder said:
I just saw this and thought that sometimes people can get a bit too carried away with their mathematical notation.

The notation seems completely fine to me. What is excessive about it? The parenthesis around the 1/12?
 
Office_Shredder said:
I just saw this and thought that sometimes people can get a bit too carried away with their mathematical notation. Hope you enjoy!

http://img695.imageshack.us/img695/9690/weirdintegralcalculatio.jpg

I don't think it's excessive. Certainly, multiplying everything out would make the integration dead simple, but his/her approach was pretty concise and interesting. Sometimes, a little extra complexity makes for a much more interesting argument (e.g. my favourite proof of the infinitude of prime numbers uses topology).
 
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