Almost A Square Tesslation

Geometry Level 1

It is well known that square tiles can easily cover the plane without overlaps or gaps.

The blue square above right is made out of a square, where a semicircle with diameter equal to the side length of the square is cut out and pasted to the side of the square. Can this shape also cover the plane without overlaps of gaps?

Yes No

Chung Kevin by Chung Kevin , 46, Australia

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2 solutions

Chung Kevin
Aug 16, 2016

We can place 4 of the shapes in the above manner, and clearly tile the plane with these squares.

12 Helpful 0 Interesting 0 Brilliant 0 Confused

Interestingly though this shaped tile cannot cover without gaps the 9x9 square figure shown in the problem .

John Clonts - 4 years, 9 months ago

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But that's not the question. The 3 by 3 square figure is to indicate that "squares can cover the plane".

Chung Kevin - 4 years, 9 months ago
Anand Chitrao
Aug 14, 2016

Connecting four of those shapes by rotating each by 90 degrees produces a rectangle

2 Helpful 0 Interesting 0 Brilliant 0 Confused

More accurately, it produces a square (which is a rectangle).

Calvin Lin Staff - 4 years, 10 months ago

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