Question

"All vertices of a convex pentagon are lattice points, and its sides have integral length. Show that its perimeter is even."

score 662 · Answer 1 · 2014-07-15 21:55:26

662

Views

"All vertices of a convex pentagon are lattice points, and its sides have integral length. Show that its perimeter is even."

Published on 15 Jul 2014 - 21:55

score 762 · Answer 2 · 2026-03-26 02:49:02

762

Views

Number of paths from $(0,0)$ to $(n,k)$ where all four directions are allowed, using a specific number of steps

Published on 26 Mar 2026 - 2:49

score 50 · Answer 3 · 2026-03-25 14:22:54

50

Views

Scalar multiple of one lattice contained in another

Published on 25 Mar 2026 - 14:22

score 368 · Answer 4 · 2014-07-23 17:20:12

368

Views

Prove that there is a basis of a lattice $\Lambda$ s.t. a reflection is of a certain form

Published on 23 Jul 2014 - 17:20

score 1.5k · Answer 5 · 2014-07-29 12:55:14

1.5k

Views

Equivalent definitions of a lattice in a real vector space of finite dimension

Published on 29 Jul 2014 - 12:55

score 398 · Answer 6 · 2026-03-25 16:03:29

398

Views

The lattice points of a f.g. rational cone form a f.g. monoid.

Published on 25 Mar 2026 - 16:03

score 846 · Answer 7 · 2014-08-06 18:20:16

846

Views

$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)

Published on 06 Aug 2014 - 18:20

score 1.5k · Answer 8 · 2014-08-10 18:05:48

1.5k

Views

Smallest linear combination of a set of vectors

Published on 10 Aug 2014 - 18:05

score 790 · Answer 9 · 2014-08-19 14:13:09

790

Views

Placing a circle in a square lattice

Published on 19 Aug 2014 - 14:13

score 155 · Answer 10 · 2014-09-04 18:41:20

155

Views

lattice symmetries portrayed in animation

Published on 04 Sep 2014 - 18:41

score 40 · Answer 11 · 2014-09-09 23:36:03

40

Views

Approximate root of $\alpha x - \beta y$ over $\mathbb Z$ except origin

Published on 09 Sep 2014 - 23:36

score 294 · Answer 12 · 2014-09-12 20:41:49

294

Views

$(a \vee b)\wedge c=b\wedge c$ implies $(c\wedge b)\wedge a= b \vee c$

Published on 12 Sep 2014 - 20:41

score 52 · Answer 13 · 2014-09-14 06:26:22

52

Views

Ehrhart Polynomials Modulo Prime Integers

Published on 14 Sep 2014 - 6:26

score 1.4k · Answer 14 · 2026-03-22 22:28:47

1.4k

Views

The number of lattice points in d-dimensional ball

Published on 22 Mar 2026 - 22:28

score 1.6k · Answer 15 · 2014-09-17 20:46:20

1.6k

Views

Number of integer lattice points within a circle

Published on 17 Sep 2014 - 20:46

List Question

"All vertices of a convex pentagon are lattice points, and its sides have integral length. Show that its perimeter is even."

Number of paths from $(0,0)$ to $(n,k)$ where all four directions are allowed, using a specific number of steps

Scalar multiple of one lattice contained in another

Prove that there is a basis of a lattice $\Lambda$ s.t. a reflection is of a certain form

Equivalent definitions of a lattice in a real vector space of finite dimension

The lattice points of a f.g. rational cone form a f.g. monoid.

$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)

Smallest linear combination of a set of vectors

Placing a circle in a square lattice

lattice symmetries portrayed in animation

Approximate root of $\alpha x - \beta y$ over $\mathbb Z$ except origin

$(a \vee b)\wedge c=b\wedge c$ implies $(c\wedge b)\wedge a= b \vee c$

Ehrhart Polynomials Modulo Prime Integers

The number of lattice points in d-dimensional ball

Number of integer lattice points within a circle

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