Figuring with Fermi Problems

• Named after the Italian-American University of Chicago professor and noted 20th century physicist and Nobel Prize-winner

• Fermi problems are math word problems that require making educated guesses using estimation skills and prior knowledge

• Fermi problems are solved by breaking the complex problem into smaller ones and using estimation skills to continuously refine your answer

So who was Enrico Fermi and what are Fermi Problems…?

One super smart dude..!

…has his own prize from the Atomic Energy Commission

…and a US stamp in his honor…

and what’s so much fun about them…?

Fermi problems require imagination Fermi problems

are good exercise for your brain

Fermi problemswill help make you

rich and famous!

Fermi problems will “force” you to think differently

You can even create your own Fermi problems and

stump your parents!

Fermi problems often don’t have an exact

answer

Let’s take a look at some examples of Fermi Problems…

I. How many basketballs would fill this classroom?

III. How many hot dogs will be sold at Yankee Stadium this season?

II. How many piano tuners are there in the

city of Chicago?

Let’s start with an easy one…Let’s start with an easy one…

some might even some might even call it a..call it a..

lay-uplay-up

Easy Question…Easy Question…

How many How many basketballs can fill basketballs can fill

this room?this room?

Easy Question…Easy Question…How many basketballs can fill this room?How many basketballs can fill this room?

what information do we need to

solve the problem…?

Talk it over for a minute….

Easy Question…Easy Question…How many basketballs can fill this room?How many basketballs can fill this room?

what information do we need to

solve the problem…?

- Volume of this room?

- Volume of a basketball?

Let’s get to work!

Volume of this room

Volume =

Length X Width X Height

Volume of this room(in inches)

Volume of a basketball?Well, a

basketball is a sphere….

And the volume of a sphere = 4/3 πr3 where r is the radius of the ball of course!

Hey old guys - use the

circumference to calculate the

radius

Volume of a basketball?Hey, don’t forget if the

circumference = 2πr, then you can find r by dividing the circumference by 2π!

Volume of a basketball?Circumference = 29.5 in = 2πr

Radius r = 29.5/(2π) = 4.69 in

Volume = (4/3) π r3

= (4/3) π (4.69)3

= 432 cubic in.

So back to the easy question…So back to the easy question…

How many basketballs can fill this room?How many basketballs can fill this room?

Answer:Divide the volume of the room by the volume of the basketball= 25,920,000 cu.in. / 432 cu.in.= 60,000 basketballsSo, how does that compare to your initial guesses?

Pictures & Music Sources:

Enrico Fermi pictures – American Institute of Physics, University of Chicago

Basketball background - Http://images.google.com/imgres?imgurl=http://static.desktopnexus.com/wallpapers/16550

Yankee Stadium - http://dianasneighborhood.files.wordpress.com/2009/07/yankee-stadium-hot-dog-permanently-scatterbrained.jpg

Piano keys - http://www.paulhahn.com/images/pianos.jpg

Basketball - http://www.barryonline.com/storage/basketball.jpg

Sweet Georgia Brown (Harlem Globetrotters) by Bobby Morganstein ProductionsFrom the Album Sports & Novelty Themes

Larry Bird & Kevin McHale http://imagecache2.allposters.com/images/pic/PHO/AAFC033~Larry-Bird-Kevin-McHale-1-Posters.jpg

Kevin Garnett http://www.thesunblog.com/gourmetgal/kevin-garnett22.jpg

Paul Pierce & Ray Allen - http://artfiles.art.com/5/p/LRG/27/2731/D3VND00Z/paul-pierce--ray-allen-game-4-of-the-2008-nba-finals.jpg