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Mar
12
comment Geometric interpretation for sum of fourth powers
@alex.jordan Did you notice the sum of squares divides sum of 4th powers? $$ \sum k^2 =\frac{1}{6}n(n+1)(2n+1) \Bigg| \sum k^4 = \frac{1}{30}n(n+1)(2n+1)(3n^2+3n-1)$$ The blog you mentioned has two solutions. One uses a triangular lattice. $$ .$$ The volume of a pyramid is $\frac{1}{3}Ah$ where $A$ is the base and $h$ is the height. By Cavalieri principle we don't worry if the Pyramid is slanted or not.
Mar
12
revised Geometric interpretation for sum of fourth powers
added 440 characters in body
Mar
12
comment Geometric interpretation for sum of fourth powers
Here is a cute article on Faulhaber's triangle
Mar
12
answered Geometric interpretation for sum of fourth powers
Mar
12
answered Common divisor of $a+b$ and $ab$.
Mar
12
reviewed Reject Question on conservative fields
Mar
12
revised continued fraction of the roots of $x^2 - \frac{53793390359}{1088391168}x + \frac{823543}{12230590464} = 0$
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Mar
12
comment continued fraction of the roots of $x^2 - \frac{53793390359}{1088391168}x + \frac{823543}{12230590464} = 0$
@MichaelBurr No I have not! Even though Vincent's theorem is the basis of the fastest method for the isolation of the real roots of polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem
Mar
12
asked continued fraction of the roots of $x^2 - \frac{53793390359}{1088391168}x + \frac{823543}{12230590464} = 0$
Mar
8
comment continued fraction of $3 + 17\sqrt{3} $
how did you know the algorithm terminated?
Mar
7
comment continued fraction of $3 + 17\sqrt{3} $
@Amzoti I took code for the GCD funciton from StackOverflow and modified it to handle algebraic numbers in $\mathbb{Z}[\sqrt{d}]$. stackoverflow.com/questions/11175131/…
Mar
7
asked continued fraction of $3 + 17\sqrt{3} $
Mar
5
revised Huzita Axiom 6 - Computing the Origami Trisection of an Angle
added 342 characters in body; edited tags; edited title
Mar
5
asked Huzita Axiom 6 - Computing the Origami Trisection of an Angle
Feb
28
comment Fast search of local positive quadruples on the sphere
cs.stackexchange.com since you are asking about runtime
Feb
28
revised Efficiently producing certain kinds of examples of the application of Euclid's algorithm
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Feb
28
revised Efficiently producing certain kinds of examples of the application of Euclid's algorithm
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Feb
28
comment Efficiently producing certain kinds of examples of the application of Euclid's algorithm
@MichaelHardy I am working on it :-) Notice gcd = 1 with probability $\frac{6}{\pi^2} \approx \frac{2}{3}$ for two random numbers! Unfortunately, these may have large factors, so they don't follow your smoothness condition.
Feb
28
revised Efficiently producing certain kinds of examples of the application of Euclid's algorithm
added 403 characters in body
Feb
28
answered Efficiently producing certain kinds of examples of the application of Euclid's algorithm