Pennies in a Tray
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Ivars Peterson (MathLand)  
What's the largest number of pennies that you can pack inside a circular tray to form a carpet of nonoverlapping coins? What about inside a square or triangular tray? What if you could expand or contract the size of all your pennies to fit a required number of them snugly in a given tray? Mathematicians have long pondered the problem of packing identical circles inside a variety of different geometric shapes. Indeed, "the optimal packing of equal disks ... is an ancient and extremely difficult problem," notes Ronald L. Graham of AT&T Laboratories. "Some of these very simple problems  like how you pack 27 discs in a triangle, square, or circle  are very stubborn."  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Articles 
Math Topics:  Conic Sections and Circles 
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