Agriculture
New Gene Fights Potato Blight
Where Have All the Bees Gone?
Seeds of the Future
Amphibians
Newts
Salamanders and Newts
Toads
Animals
A Tongue and a Half
Saving Africa's Wild Dogs
Ultrasonic Frogs Raise the Pitch
Behavior
Fear Matters
Copycat Monkeys
Giving Sharks Safe Homes
Birds
Crows
Pheasants
Cardinals
Chemistry and Materials
The science of disappearing
The Taste of Bubbles
Butterfly Wings and Waterproof Coats
Computers
Play for Science
Electronic Paper Turns a Page
The Shape of the Internet
Dinosaurs and Fossils
South America's sticky tar pits
Some Dinos Dined on Grass
A Dino King's Ancestor
E Learning Jamaica
Results of GSAT are in schools this week
2014 GSAT Results for Jamaican Kids
E Learning in Jamaica WIN PRIZES and try our Fun Animated Games
Earth
Springing forward
Arctic Algae Show Climate Change
Earth from the inside out
Environment
Forests as a Tsunami Shield
Plant Gas
Blooming Jellies
Finding the Past
Prehistoric Trips to the Dentist
Digging Up Stone Age Art
Chicken of the Sea
Fish
Great White Shark
Piranha
Halibut
Food and Nutrition
Moving Good Fats from Fish to Mice
The Color of Health
How Super Are Superfruits?
GSAT English Rules
Who vs. Whom
Who vs. That vs. Which
Pronouns
GSAT Exam Preparation Jamaica
E Learning in Jamaica WIN PRIZES and try our Fun Animated Games
GSAT Exam Preparation
The Annual GSAT Scholarships
GSAT Exams Jamaica Scholarships
GSAT Scholarship
GSAT Practice Papers | GSAT Mathematics | Maths
Results of GSAT are in schools this week
GSAT Mathematics
Secrets of an Ancient Computer
How a Venus Flytrap Snaps Shut
Detecting True Art
Human Body
Taste Messenger
A Better Flu Shot
Gut Microbes and Weight
Invertebrates
Fleas
Crawfish
Butterflies
Mammals
Black Bear
Beavers
African Wild Dog
Parents
Raise a Lifelong Reader by Reading Aloud
What Not to Say to Emerging Readers
Choosing a Preschool: What to Consider
Physics
Project Music
Black Hole Journey
Gaining a Swift Lift
Plants
Plants Travel Wind Highways
Cactus Goo for Clean Water
White fuzzy mold not as friendly as it looks
Reptiles
Sea Turtles
Alligators
Copperhead Snakes
Space and Astronomy
Sun Flips Out to Flip-Flop
Rover Makes Splash on Mars
A Puffy Planetary Puzzle
Technology and Engineering
Roll-Up Computer Monitors to Go
Supersuits for Superheroes
Morphing a Wing to Save Fuel
The Parts of Speech
Adjectives and Adverbs
What is a Preposition?
What is a Verb?
Transportation
Flying the Hyper Skies
Ready, unplug, drive
Tinkering With the Basic Bike
Weather
Arctic Melt
Warmest Year on Record
A Dire Shortage of Water
Add your Article

How to Slice a Cake Fairly

Sharing can be hard. Every kid knows that, and mathematicians do, too. So mathematicians have spent a lot of time thinking about how to make sharing easier. Mathematicians are particularly fond of sharing birthday cake. Not just any birthday cake, but one with lots of icing and various decorations, with nuts here and coconut there. Then they ask, if two people like different parts of the cake better, how can they divide the cake into two pieces so that they're both satisfied with the piece that they each get? There's an old solution known as "I cut, you choose." You start by cutting the cake into two pieces that you like equally well. Then your friend picks the one that she prefers. The two pieces don't have to be the same size. If you particularly like nuts, for example, you might make the piece with fewer nuts bigger, so that you'd be happy no matter which piece your friend chose. You'd end up with either a smaller piece with lots of nuts or a larger piece with fewer nuts. But Steven Brams of New York University doesn't think that's fair. When you're done, you get a piece that you might think is worth half the value of the cake. But your friend might think that she got much more than half the value of the cake. For example, suppose that your friend really likes coconut, and the bigger, less nutty piece has lots of coconut. Then she'll think that she's gotten a really great deal. She got not only more cake but also the best part! Brams says that a division should be considered fair only if two people think they both got pieces of the same value. He's worked out a new procedure for cake-cutting that makes this happen. Here's how it works. You and your friend would each tell your mom where you would divide the cake into two pieces. If the two of you happen to pick the same spot, she'd simply divide the cake at that spot. Both of you would be equally happy with your shares. But suppose the two spots are different. If your spot were to the left of your friend's spot, you'd get the piece to the left of your spot. Your friend would get the piece to the right of her spot. And there'd be a piece left over in the middle. Your mom would then split the middle section between you and your friend. That way, you each get a piece that you value equally—plus a bonus! It's a neat idea, but is such a procedure practical? Would you use it? "I don't know if anyone other than me has actually brought a cake in and tried to divide it," says James Tanton, a mathematics teacher at St. Mark's School in Southborough Mass. Such schemes often don't work in practice. "Human beings are too fuzzy," he says. "They change their minds."—J.J. Rehmeyer

How to Slice a Cake Fairly
How to Slice a Cake Fairly








Designed and Powered by HBJamaica.com™