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 (9-12), College|
|Math Topics:||Conic Sections and Circles|
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