Pizza Ordering Dilemma

You are hungry. You are reading the menu in a pizzeria and you hesitate whether to order one large pizza, or two smaller. Both choices costs the same, so the dilemma is which one to order.

This animation shows one easy method for solving the problem. The method is the following: make a triangle from the pizzas. If the triangle is right, then the large pizza is as big as the two smaller ones. Why?

Let the diameters of the pizzas are S (for the small), M (for the medium) and L (for the large). Imagine the two smaller pizzas are one medium and one small. If the triangle made of the halves of the three pizzas is right, then according to the Pythagorean Theorem:

S² + M² = L².

Then we can multiply by ¼π and we get:

¼πS² + ¼πM² = ¼πL²,

which is equivalent to:

π(½S)² + π(½M)² = π(½L)².

However, the terms in this equation are exactly the areas of the pizzas, because the area of a circle with diameter d is π(½d)². So, we find that if the triangle is right, then the large pizza is as big as the medium and the small combined.

But still there is one unresolved issue. How to find out whether an angle is right? That's simple. If we can fit a quarter of a pizza in the angle, then it is a right one.

And here is a challenge for you: if the triangle is not right, then how to find whether the large pizza is bigger or smaller than the other two?

Category:

Education

Tags:

• Elica
• Logo
• demo
• pizza
• order
• dilemma
• solution
• math
• triangle
• Pythagoras
• Pythagorean

[simondegrootpuntnl]

Great education idea: Give the students real pizza's and let them figure this out...

[dwyllie]

Great!

[tuba1423]

First!