The number Pi is a mathematical constant. It represents the ratio of the circumference of a circle to its diameter. If you divide the circumference of any circle (or perfectly-formed, hand-tossed pizza) by its diameter (the measure of a straight line cutting the pizza in half), you will get Pi, which is equal to 22/7, or approximately 3.14. Now let's review Fabian's quandary, from a couple of days ago...

__Background__:

Fabian Focaccia (not his real name, which is Sal Monella) is a struggling 'artist' who is working at a neighborhood pizzeria in Brooklyn, New York (not his real location, as he is in the Federal Witness Protection Program, but which is still the best geographical location to make a pizza purchase if you/ youse should ever get around to it) to pay his bills until he can sell one of his paintings. He is faced with a decision and needs your help. He has cardboard boxes for 'take out' pizza (this pizza parlor does a

*big*take-out business -- even for Arizona...oops!) which are each three inches deep (irrelevant for solving this problem) and measure exactly 20 inches by 20 inches square.

__The Pizza Box Puzzle (In Two Parts)__:

1) What is the circumference of the largest pizza (assume that it is hand-tossed and perfectly round) which can be placed in the box

*neatly*, i.e., placing it flat without stuffing it in and distorting its perfect shape?

__: This is really just a circle inscribed in a square. Here's a picture:__

**Answer**As you can see, the diameter of the pizza must be exactly 20" for it to fit snugly in the box. If that's the case, then the pizza would have a circumference equal to Pi times the diameter, or approximately

**62.8"**.

and,

2) What is the circumference of the largest individual pie (out of two) which can be placed in the box if two pies of equal size are placed in a cardboard container of the same dimensions as in number 1, above?

__: This is very similar to the first question. But this time you've got to put two equally-sized pies in the box without mutilating them. Here's a picture:__

**Answer**The two pies, side by side,

*can still not have combined diameters greater than the 20" length of the box*(some of you were going to try doing this using the hypotenuse obtained by cutting the box into two right triangles, but that doesn't work - ha!). Each of the two pies will have a diameter of

**10"**, and each will have a corresponding circumference of

**31.4**".

BCNU soon.

Douglas E Castle

(http://aboutDouglasCastle.blogspot.com)

Don't forget to maintain that brain!

*Braintenance!*(http://Braintenance.blogspot.com)

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