Wavy Curvy

Geometry Level 1

Can we tile the plane with these purple tiles?

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Chung Kevin by Chung Kevin , 45, Australia

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3 solutions

Andy Hayes
Oct 28, 2017

Here is one way to tile a plane with the purple shapes:

You could fill in as much of the plane as you like with these tiles.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Junyi Liu
Oct 17, 2017

Let's assumed that this graphing is drawn to scale, so this graphing is a graphing fit the rules of rotational symmetry, so this guarantee that its top can fit its bottom perfectly, their sides fits too.So we can tile the plane with these tiles.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Rotational symmetry doesn't guarantee that the top can fit the bottom perfectly. E.g. a circle has rotational symmetry, but doesn't fit properly.

Chung Kevin - 3 years, 7 months ago

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Rotational symmetry does guarantee that the top can fit the bottom perfectly but do NOT guarantee that they can fill up a plane without overlap or gap.

Junyi Liu - 3 years, 7 months ago
Samir Betmouni
Dec 3, 2017

The shape fits with itself in columns and, most importantly:

Tiling a plane and tiling a room are two different things!

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