Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Amicable Triangle and Rectangles on the Integer Lattice

Iwan Praton, Weiran Zeng

Abstract

Two polygons are amicable if the perimeter of one is equal to the area of the other and vice versa. A polygon is a lattice polygon if its vertices are on the integer lattice $\Z^2$. We show that there is one pair of amicable lattice triangles and five pairs of amicable lattice rectangles.

Amicable Triangle and Rectangles on the Integer Lattice

Abstract

Two polygons are amicable if the perimeter of one is equal to the area of the other and vice versa. A polygon is a lattice polygon if its vertices are on the integer lattice . We show that there is one pair of amicable lattice triangles and five pairs of amicable lattice rectangles.

Paper Structure

This paper contains 2 sections, 4 theorems, 2 equations.

Table of Contents

  1. Triangles
  2. Rectangles

Key Result

Theorem 1

There is exactly one pair of amicable lattice triangles.

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 4
  • proof