Translative Covering a Square with Isosceles Right Triangles

Key Points

• This research explores the conditions under which isosceles right triangles can cover a rectangle through translative methods.
• Investigated the covering of a rectangle using homothetic copies of right isosceles triangles.
• Analyzed area requirements for successful coverage of squares and rectangles.
• Established strict bounds for the area of triangles needed for coverage.
• Any collection of equal triangles with a total area of at least 2 allows for a 1×1 covering.
• A total area of at least 3 from positive homothetic triangles also enables a 1×1 covering.
• For rectangles with dimensions satisfying a≥5+334b, an area of at least 12(a+b)² ensures coverage.

Abstract