There are 15 types of pentagons that can “tile the plane”. The most recent was found very recently, and was the first such discovery in 30 years.

Check it out here: http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/aug/10/attack-on-the-pentagon-results-in-discovery-of-new-mathematical-tile

BADGING: Read the article. Write a sentence (in your own words) explaining what it means for a shape to “tile the plane”. Pick two of the pentagon tiles shown in the article and copy out what it looks like when they “tile the plane”. Compare and contrast the two tilings — what do the two tilings have in common (besides the fact that they’re pentagons)? What is different about them?

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