MATHEMATICS OF BUYING A PIZZA:Ordering one large pizza better than two mediums

 

If you put a circle inside a square, it fills ~78.5% of the space. This is true whether the square is large or small.

If you have an 18" square, you can put an 18" pizza in it, or four 9" pizzas, and they take up the same percentage of the space. Therefore an 18" pizza is four times as large as a 9" pizza.

That makes an 18" pizza twice as much as two 9" pizzas. There is nothing special about the circular shape, though. You could cut the pizzas as stars, crescents, ovals, etc. The same argument works; it's a fact about two-dimensional objects, not about circles or pizzas

3.1415926... and Pizza

A Chinese tourist came to Canada to see maple leaves in fall. He ordered a 9" diameter pizza for lunch at a tourist spot. After a while, the waiter brought two of 5" diameter pizzas and said apologetically "Sorry Sir, we are running out of 9" pizza. Here are two of 5" pizzas to make up your order with one extra inch as our courtesy".

The tourist was surprised. He invited the waiter and the restaurant manager to his table and started demonstrating the circle area calculation:

Where Pie is approximately 3.1415926..., the circumference of any circle divided by its diameter; r is the radius.The area of a 9” pizza = 63.62 square inches; the area of a 5” pizza = 19.63 square inches."The area of two 5" pizza = 39.26 square inches. Three of 5" pizzas could not make up my order. How could you offer me 1" extra free pizza?", the tourist reasoned.The restaurant manager was so amazed. He offered 4 pizzas to the tourist, "wow, you people are so marvellous, politicians know how to take bribes, citizens know how to protect themselves...".This is a joke my friend shared with me from Wechat. We often take for granted for something sounds like common sense, but actually doesn't make sense if you stop to think about it.Food for thought. Happy Easter!