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Nov
20
comment What is the Beta-Function used for in Calculus?
google.com/…
Nov
20
comment Why does the fundamental theorem of calculus work?
@mike4ty4 : 1.About $\pi$, if it is defined as the ratio of diameter to perimeter, or area to radius, then $\pi$ depends on the geometry 2.If $\pi$ is suppose to be a constant $3.14...$ then yes of course it does not change! because it is defined as a specific constant not a ratio 2. About the FTC, it is only valid with Eucliedean metric, but never explicitly stated.
Nov
20
comment Why does the fundamental theorem of calculus work?
@hurkyl , then how come if one changes the metric that a graph is drawn in, then the relation with area under the graph is no longer as simple as FTC? the difference here is the metric of euclidean space, otherwise it would not be a just simple difference.
Nov
20
comment Why does the fundamental theorem of calculus work?
@vectomaut : does FTC hold in non euclidean geometries? or non euclidean metrics? or are they implicitly assume the euclidean metric. this version of FTC does not hold with non euclidean metric.
Nov
20
comment Why does the fundamental theorem of calculus work?
It only works with Euclidean metric, there are many hidden assumptions that I have not seen stated explicitly, this is special case of more generalized theorems, additional assumptions simplify it to the form known as FTC, If you are really interested in the Whys, then look up real and complex analysis.
Nov
20
comment Why does the fundamental theorem of calculus work?
khanacademy.org/math/integral-calculus/…
Nov
18
revised Simple examples of applications of converse, contrapositive and inverse used in mathematical proofs rather than logic.
edited tags
Nov
18
asked Simple examples of applications of converse, contrapositive and inverse used in mathematical proofs rather than logic.
Nov
18
revised $\int \frac{\sin^3x}{\sin^3x + \cos^3x)}$?
edited title
Nov
17
comment Finding a sequence satisfying this recurrence relation?
Where the hell is at least one upvote for this beautiful answer?
Nov
17
comment How could I generate this sequence?
no skill required, lagrange interpolation is all is needed.
Nov
17
comment Is infinite binary operation for zeros 0+0…+0 well defined math object?
good question, voting to reopen and +1.
Nov
14
revised How to prove $\tan^{-1}(x)+\tan^{-1}(\frac{1}{x}) = \frac{\pi}{2}$?
edited title
Nov
13
comment What is the correct term for the “major axis” of an oblong?
@spaceiver , yes you are correct, my bad.
Nov
13
comment How to abbreviate $a_0=a_1=\cdots=a_n$?
I really like your first suggested notation, that will also work with equality replaced by many other relation or operator symbols, it is simple and intuitive and preferable to set based hickery pokery IMHO.
Nov
13
comment What is the correct term for the “major axis” of an oblong?
diagonal is the keyword, not axis
Nov
12
accepted Convergence rate for $a_{n+1}=\sqrt{2 \sqrt {a_n}}$?
Nov
12
revised Convergence rate for $a_{n+1}=\sqrt{2 \sqrt {a_n}}$?
added 161 characters in body
Nov
12
comment Convergence rate for $a_{n+1}=\sqrt{2 \sqrt {a_n}}$?
@ClaudeLeibovici : I try that, dont know why though.
Nov
12
comment Convergence rate for $a_{n+1}=\sqrt{2 \sqrt {a_n}}$?
@Omnomnomnom : no, just somthing I cooked up, might no simple answer.