Dissections of trapezoids into trapezoids homothetic to trapezoids of a given set

TL;DR

This paper presents new theorems on tiling trapezoids with specific base relations, expanding understanding of geometric dissections involving homothetic trapezoids within certain algebraic number fields.

Contribution

It introduces several theorems on trapezoid tilings, focusing on cases with rational and quadratic number field base relations, advancing geometric dissection theory.

Findings

Theorem on trapezoids with rational base relation

Results on trapezoids with base relation from quadratic number fields

Enhanced understanding of trapezoid tilings in algebraic contexts

Abstract

Here I present several theorems about trapezoids tilings. The first one is related to trapezoids with rational base relation, the other ones are related to those with base relation from quadratic number field.