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edited Feb 21 2011 at 3:30 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels. Another algorithms of integer linear programming: finding a “closest points” in a given halfplane (added by Wilberd van der Kallen).
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
14) Bach and Shallit show how to compute the Jacobi symbol in terms of the simple continued fraction (Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.)
15) A criterion for a rectangle to be tilable by rectangles of a similar shape. Construction of alternating-current circuits with given properties (added by M. Skopenkov).
16) Slam dunking of rational surgery diagrams for a three-manifolds (added by Kelly Davis).
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edited Feb 21 2011 at 3:04 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels. Another algorithms of integer linear programming: finding a “closest points” in a given halfplane (added by Wilberd van der Kallen); finding a “closest points” in a given angle.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
14) Bach and Shallit show how to compute the Jacobi symbol in terms of the simple continued fraction (Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.)
15) A criterion for a rectangle to be tilable by rectangles of a similar shape. Construction of alternating-current circuits with given properties (added by M. Skopenkov).
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edited Feb 21 2011 at 2:53 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels. Another algorithms of integer linear programming: finding a “closest points” in a given halfplane (added by Wilberd van der Kallen); finding a “closest points” in a given angle.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
14) Bach and Shallit show how to compute the Jacobi symbol in terms of the simple continued fraction (Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.)
15) A criterion for a rectangle to be tilable by rectangles of a similar shape. Construction of alternating-current circuits with given properties (added by M. Skopenkov).
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edited Feb 21 2011 at 2:21 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
14) Bach and Shallit show how to compute the Jacobi symbol in terms of the simple continued fraction (Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.)
15) A criterion for a rectangle to be tilable by rectangles of a similar shape. Construction of alternating-current circuits with given properties (added by M. Skopenkov).
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edited Feb 20 2011 at 16:41 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
14) Bach and Shallit show how to compute the Jacobi symbol in terms of the simple continued fraction (Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.)
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edited Feb 20 2011 at 6:53 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, number recognition (Andreas Blass), parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
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edited Feb 20 2011 at 6:48 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
13) Analysis of Lehmer pseudo-random number generator (added by Gerry Myerson).
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edited Feb 20 2011 at 2:08 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) The way to attack (discovered by Michael J. Wiener) RSA public key crypto system with small private exponents (added by jp).
12) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
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edited Feb 20 2011 at 2:00 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
11) DDA-algorithm for converting a segment into a nice-looking sequence of pixels.
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edited Jan 3 2011 at 5:43 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
9) Calculation of the number of A-graded algebras (V.I. Arnold A-graded algebras and continued fractions)
10) Asymptotic behavior of a curve in $\mathbb{R}^n$ with constant curvature $k_1$, constant second curvature $k_2$, ... (till constant curvature $k_{n-1}$). (V.I. Arnold)
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edited Jan 3 2011 at 5:27 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
8) Calculation of Dedekind sums.
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edited Dec 20 2010 at 10:44 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.)
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of rational tangles (added by Paolo Aceto).
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edited Dec 19 2010 at 14:09 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything?
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$ ad-bc=N$, calculation of convex hull of non-zero lattice points from first quadrant etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Calculation of convex hull Singularitie resolution in toric surfaces (added by J.C. Ottem).
7) Classification of non-zero lattice points from first quadrantrational tangles (added by Paolo Aceto).
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edited Dec 19 2010 at 12:19 |
I know some applications of finite continued fractions. Probably you know more. Can you add anything?
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$ etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
6) Calculation of convex hull of non-zero lattice points from first quadrant.
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edited Dec 19 2010 at 10:49 |
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Post Made Community Wiki by Alexey Ustinov
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occurred Dec 19 2010 at 10:47
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asked Dec 19 2010 at 9:56 |
Applications of finite continued fractions
I know some applications of finite continued fractions. Probably you know more. Can you add anything?
1) (Trivial) Analysis of Euclidean algorithm (and its variants). This item includes extended Euclidean algorithm, calculation of $a^{-1}\pmod n$, lattice reduction, parametrization of solution of the equation $ad-bc=N$ etc.
2) Decomposition of prime $p=4n+1$ to the sum of two squares.
3) Rodseth's formula for Frobenius numbers with three arguments.
4) Analysis of Frieze Patterns from The Book of Numbers (Conway, J. H. and Guy, R. K.)
5) Calculation of goodness (dicrepancy or something similar) of 2-dimesional lattice rules for numerical integration.
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