Question

Show that for every non-zero polynomial $p$ in $3$ variables, there are at most degree $p$ contained in the set of zeros of $p$

score 104 · Answer 1 · 2021-05-25 13:40:34

104

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Show that for every non-zero polynomial $p$ in $3$ variables, there are at most degree $p$ contained in the set of zeros of $p$

Published on 25 May 2021 - 13:40

score 63 · Answer 2 · 2026-03-26 02:56:05

63

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What is the reason for this step in proving the Borsuk-Ulam Theorem (by triangulation)

Published on 26 Mar 2026 - 2:56

score 34 · Answer 3 · 2026-03-27 14:56:45

34

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Let $A_1,\dots,A_k \subset \mathbb{R}^n$. If $x \in \text{conv}(A_1+…+A_k)$, then $x \in \text{conv}(A_1’+…+A_k’)$, with finite $A_i’ \subset A_i$.

Published on 27 Mar 2026 - 14:56

score 46 · Answer 4 · 2026-03-27 14:53:40

46

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Let $K,L$ be convex bodies in $\mathbb{R}^n$ s.t. $(K \cup L)$ is convex. If $x \in K, y \in L$, then $[x,y] \cap (K \cap L) \neq \emptyset$.

Published on 27 Mar 2026 - 14:53

score 153 · Answer 5 · 2021-06-07 20:04:20

153

Views

Definition of the volume functional of convex and star bodies.

Published on 07 Jun 2021 - 20:04

score 143 · Answer 6 · 2021-06-16 09:35:36

143

Views

What are some good informal beginner level books for studying combinatorial geometry?

Published on 16 Jun 2021 - 9:35

score 52 · Answer 7 · 2026-03-25 20:53:14

52

Views

Counting the number of facets of the alternating sign matrix polytopes ($ASM_n$).

Published on 25 Mar 2026 - 20:53

score 97 · Answer 8 · 2021-06-24 13:53:05

97

Views

Doubt regarding a lemma

Published on 24 Jun 2021 - 13:53

score 42 · Answer 9 · 2021-07-16 21:07:34

42

Views

What kind of isometric embedding is this?

Published on 16 Jul 2021 - 21:07

score 119 · Answer 10 · 2026-03-26 17:35:51

119

Views

Discrete Geometry Violating The Triangle Inequality

Published on 26 Mar 2026 - 17:35

score 62 · Answer 11 · 2021-07-28 10:55:31

62

Views

Covering of a polytope by $p$-balls with $p\geq 2$

Published on 28 Jul 2021 - 10:55

score 500 · Answer 12 · 2021-08-09 11:54:22

500

Views

Find ellipse of maximum area which is entirely contained within the area defined by a set of points

Published on 09 Aug 2021 - 11:54

score 31 · Answer 13 · 2021-08-11 11:05:15

31

Views

Covering of hyperplane $\{x: \langle v, x\rangle =0\}$ by balls around $(I-\frac{vv^T}{\langle v,v\rangle})\mathbb Z^n$

Published on 11 Aug 2021 - 11:05

score 448 · Answer 14 · 2026-03-27 08:39:40

448

Views

Finding a triangle that contains a given point

Published on 27 Mar 2026 - 8:39

score 37 · Answer 15 · 2021-08-31 05:26:18

37

Views

How can we find the "dimension" of a non-continuous "tiled" space?

Published on 31 Aug 2021 - 5:26

List Question

Show that for every non-zero polynomial $p$ in $3$ variables, there are at most degree $p$ contained in the set of zeros of $p$

What is the reason for this step in proving the Borsuk-Ulam Theorem (by triangulation)

Let $A_1,\dots,A_k \subset \mathbb{R}^n$. If $x \in \text{conv}(A_1+…+A_k)$, then $x \in \text{conv}(A_1’+…+A_k’)$, with finite $A_i’ \subset A_i$.

Let $K,L$ be convex bodies in $\mathbb{R}^n$ s.t. $(K \cup L)$ is convex. If $x \in K, y \in L$, then $[x,y] \cap (K \cap L) \neq \emptyset$.

Definition of the volume functional of convex and star bodies.

What are some good informal beginner level books for studying combinatorial geometry?

Counting the number of facets of the alternating sign matrix polytopes ($ASM_n$).

Doubt regarding a lemma

What kind of isometric embedding is this?

Discrete Geometry Violating The Triangle Inequality

Covering of a polytope by $p$-balls with $p\geq 2$

Find ellipse of maximum area which is entirely contained within the area defined by a set of points

Covering of hyperplane $\{x: \langle v, x\rangle =0\}$ by balls around $(I-\frac{vv^T}{\langle v,v\rangle})\mathbb Z^n$

Finding a triangle that contains a given point

How can we find the "dimension" of a non-continuous "tiled" space?

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