User hatch22

19 votes

3 answers

3k views

Why does rational trigonometry not work over a field of Characteristic 2?

asked Mar 18, 2013 at 18:03

14 votes

4 answers

2k views

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

asked Jan 5, 2015 at 19:57

8 votes

2 answers

530 views

What transcendental numbers are produced by $\sin{\alpha}$ when $\alpha$ is algebraic/constructible/rational (in radians)?

asked Jul 8, 2014 at 15:21

7 votes

1 answer

1k views

How does trigonometry in a Galois field work?

asked Mar 19, 2013 at 13:31

5 votes

2 answers

2k views

Is the continued fraction of the square root of a base $\phi$ (golden ratio) number periodic when the continued fraction is expressed in base $\phi$?

asked Jul 16, 2012 at 20:41

5 votes

2 answers

653 views

Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

asked Jul 1, 2014 at 15:13

5 votes

1 answer

209 views

Are the ring of integers of the constructible numbers a Euclidean domain?

asked Aug 18, 2015 at 13:49

5 votes

1 answer

1k views

When is $\mathbb Z[\zeta_n]$ a Euclidean Domain?

asked Sep 18, 2017 at 17:28

3 votes

1 answer

238 views

Are some Lucas numbers always coprime with all previous Lucas numbers?

asked May 29, 2014 at 21:19

2 votes

0 answers

136 views

How accurately can a irrational algebraic number represent a different irrational number compared to a rational approximation?

asked Feb 16, 2013 at 20:25

2 votes

1 answer

143 views

For integers $a$ and $b \gt 0$, and $n^2$ a sum of two square integers, does this strategy find the largest integer $x | x^2 \lt n^2(a^2 + b^2)$?

asked Oct 4, 2012 at 17:48

2 votes

0 answers

176 views

Are there 3D tilings of a 3D projective hyperplane or 3-sphere?

asked Mar 21, 2013 at 20:42

2 votes

1 answer

1k views

Formula for how many combinations of powers of 2 sum to $2^n$

asked Oct 19, 2015 at 14:40

2 votes

2 answers

164 views

What is a field with bounded whole and unbounded fractional part called?

asked Nov 16, 2015 at 21:46

2 votes

0 answers

198 views

Lower bounds on possible integer relations from the PSLQ algorithm

asked Feb 12, 2015 at 17:05

2 votes

0 answers

131 views

Under what conditions is a tower of quadratic extensions a UFD, GCD domain, or just an Integral Domain?

asked Mar 8, 2015 at 19:51

1 vote

0 answers

49 views

Monadic Second-order Logic of 2 Successors and Binary Tree Automata

asked Apr 13, 2020 at 21:15

1 vote

1 answer

56 views

In what way is a quadratic extention to a finite field isomorphic to a finite field of higher order?

asked Nov 17, 2015 at 16:05

1 vote

0 answers

538 views

When are the integers extended with the nth root of unity a unique factorization domain? [duplicate]

asked Sep 18, 2017 at 15:29

1 vote

1 answer

122 views

Why is the set of all true first-order statements about non-negative integers in the language with only equality, $+$ and $\times$ undecidable?

asked Jan 23, 2015 at 17:22

1 vote

1 answer

396 views

What is the smallest fraction produced by a sum of fractions with bounded denominator?

asked Feb 2, 2015 at 4:21

1 vote

1 answer

663 views

Closest rational approximation of $\sqrt x$ with denominator having prime powers $\lt n$

asked Feb 5, 2015 at 15:53

1 vote

1 answer

422 views

How do I determine appropriate rational approximations to a sum of square roots in order to bound the error accumulation?

asked Jan 8, 2013 at 3:27

0 votes

0 answers

119 views

How is Lagrange's $2\sqrt{D}$ bound on partial denominators proven for periodic regular continued fractions of quadratic irrationals

asked Jan 16, 2015 at 17:02

Stack Exchange Network

24 Questions

Why does rational trigonometry not work over a field of Characteristic 2?

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

What transcendental numbers are produced by $\sin{\alpha}$ when $\alpha$ is algebraic/constructible/rational (in radians)?

How does trigonometry in a Galois field work?

Is the continued fraction of the square root of a base $\phi$ (golden ratio) number periodic when the continued fraction is expressed in base $\phi$?

Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

Are the ring of integers of the constructible numbers a Euclidean domain?

When is $\mathbb Z[\zeta_n]$ a Euclidean Domain?

Are some Lucas numbers always coprime with all previous Lucas numbers?

How accurately can a irrational algebraic number represent a different irrational number compared to a rational approximation?

For integers $a$ and $b \gt 0$, and $n^2$ a sum of two square integers, does this strategy find the largest integer $x | x^2 \lt n^2(a^2 + b^2)$?

Are there 3D tilings of a 3D projective hyperplane or 3-sphere?

Formula for how many combinations of powers of 2 sum to $2^n$

What is a field with bounded whole and unbounded fractional part called?

Lower bounds on possible integer relations from the PSLQ algorithm

Under what conditions is a tower of quadratic extensions a UFD, GCD domain, or just an Integral Domain?

Monadic Second-order Logic of 2 Successors and Binary Tree Automata

In what way is a quadratic extention to a finite field isomorphic to a finite field of higher order?

When are the integers extended with the nth root of unity a unique factorization domain? [duplicate]

Why is the set of all true first-order statements about non-negative integers in the language with only equality, $+$ and $\times$ undecidable?

What is the smallest fraction produced by a sum of fractions with bounded denominator?

Closest rational approximation of $\sqrt x$ with denominator having prime powers $\lt n$

How do I determine appropriate rational approximations to a sum of square roots in order to bound the error accumulation?

How is Lagrange's $2\sqrt{D}$ bound on partial denominators proven for periodic regular continued fractions of quadratic irrationals