Question

Does the $n$-sphere have a surjective rational parameterization $p \colon \mathbb{R}^k \to S^n$ for some $k \geq 1$?

score 152 · Answer 1 · 2026-03-25 14:47:05

152

Views

Does the $n$-sphere have a surjective rational parameterization $p \colon \mathbb{R}^k \to S^n$ for some $k \geq 1$?

Published on 25 Mar 2026 - 14:47

score 31 · Answer 2 · 2022-10-21 15:09:29

31

Views

Represent a rational function

Published on 21 Oct 2022 - 15:09

score 34 · Answer 3 · 2022-10-21 18:22:25

34

Views

Representation of rational functions

Published on 21 Oct 2022 - 18:22

score 36 · Answer 4 · 2022-10-25 22:28:35

36

Views

Asymptotics of rational functions intersecting with generalized arithmetic progressions

Published on 25 Oct 2022 - 22:28

score 22 · Answer 5 · 2026-03-29 16:02:49

22

Views

What are the possible orders of rational functions under composition (with coefficients in the reals)?

Published on 29 Mar 2026 - 16:02

score 41 · Answer 6 · 2022-10-27 19:51:56

41

Views

Having much trouble trying to solve a rational equation with exponentials in each denominator

Published on 27 Oct 2022 - 19:51

score 46 · Answer 7 · 2022-10-29 19:04:50

46

Views

How should I think about points of discontinuity of rational functions?

Published on 29 Oct 2022 - 19:04

score 141 · Answer 8 · 2022-10-31 17:31:58

141

Views

Why is the function $f(x) = e^x$ not a rational function?

Published on 31 Oct 2022 - 17:31

score 172 · Answer 9 · 2022-11-03 02:51:04

172

Views

Graphing Rational Functions: Identifying the equation

Published on 03 Nov 2022 - 2:51

score 45 · Answer 10 · 2022-11-11 12:54:18

45

Views

Upper-bound for positive roots of $\sum_{j=1}^d 1 / (x + \lambda_j) = c$, where the $\lambda_j$'s are fixed nonnegative reals

Published on 11 Nov 2022 - 12:54

score 51 · Answer 11 · 2022-11-14 09:55:00

51

Views

How to graph manually the rational functions of the form $f(x)=\frac{x+1}{2x^2+1}$

Published on 14 Nov 2022 - 9:55

score 19 · Answer 12 · 2022-11-15 14:45:40

19

Views

What are the "ordinary" rational functions from Weierstrass tangent substitution?

Published on 15 Nov 2022 - 14:45

score 192 · Answer 13 · 2022-11-16 13:29:54

192

Views

Proving that an integral defines a rational function without evaluating

Published on 16 Nov 2022 - 13:29

score 683 · Answer 14 · 2022-11-21 01:08:02

683

Views

Where does this approximation for $2^x-1$ come from?

Published on 21 Nov 2022 - 1:08

score 44 · Answer 15 · 2022-11-25 01:45:35

44

Views

What method should I use to solve rational equations like this for a different quantity?

Published on 25 Nov 2022 - 1:45

List Question

Does the $n$-sphere have a surjective rational parameterization $p \colon \mathbb{R}^k \to S^n$ for some $k \geq 1$?

Represent a rational function

Representation of rational functions

Asymptotics of rational functions intersecting with generalized arithmetic progressions

What are the possible orders of rational functions under composition (with coefficients in the reals)?

Having much trouble trying to solve a rational equation with exponentials in each denominator

How should I think about points of discontinuity of rational functions?

Why is the function $f(x) = e^x$ not a rational function?

Graphing Rational Functions: Identifying the equation

Upper-bound for positive roots of $\sum_{j=1}^d 1 / (x + \lambda_j) = c$, where the $\lambda_j$'s are fixed nonnegative reals

How to graph manually the rational functions of the form $f(x)=\frac{x+1}{2x^2+1}$

What are the "ordinary" rational functions from Weierstrass tangent substitution?

Proving that an integral defines a rational function without evaluating

Where does this approximation for $2^x-1$ come from?

What method should I use to solve rational equations like this for a different quantity?

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