Cool Fuel Cells

Astronauts have been using them for power aboard spacecraft since the 1960s. Soon, perhaps, they'll be just as common on Earth--powering cars, trucks, laptop computers and cell phones. They're called fuel cells. By combining hydrogen fuel with oxygen, fuel cells can produce plenty of electric power while emitting only pure water as exhaust. They're ...

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What's So Bad About The Badlands?

Hundreds of square miles of South Dakota are known as 'Badlands', a dry terrain of colorful rock formations and little vegetation. For pioneers crossing them in the 19th century, these lands were ... Continue reading


A River of Sand

Next time you're at the beach or in the desert, climb a sand dune in bare feet on a windy day. Stand still in various places on the gently sloping windward side. Watch how wind-driven sand grains ... Continue reading


GPS (Global Positioning System)

The GPS, or Global Positioning System, is the high-tech application of one of the most fundamental principles of geometry. Surveyors routinely use geometry and triangulation to map and lay out areas ... Continue reading


How Fast is Mach 1?

A Mach number is a common ratio unit of speed when one is talking about aircrafts. By definition, the Mach number is a ratio of the speed of a body (aircraft) to the speed of sound in the undisturbed ... Continue reading


Perfect Numbers

PerfectNumbersSome numbers are more special than others. According to Pythagoras (569 BC - 475 BC) and Euclid (325 BC - 265 BC), some are so special that they called them mystical or perfect numbers. The first perfect number is 6; the second is 28. The Greeks knew of two more: 496 and 8,128. Can you see a pattern? Try figuring out what is so special about these four numbers before you continue reading.

Well, the definition of a perfect number is: any number that is equal to the sum of its divisors (numbers that will divide into it without leaving a remainder). Therefore you can see that: 6 = 1 + 2 + 3; 28 = 1 + 2 + 4 + 7 + 14; and so on. Simple, right? How about the fifth perfect number? Can you come up with it? Don't even try … just continue reading.

It took mathematicians about 1,500 years (1536, Hudalrichus Regius) to discover the fifth perfect number: 33,550,336. The greatest contributions to future discoveries of perfect numbers were offered by French mathematicians Fermat and Mersenne, during early 1600s, when they devised a useful formula for finding perfect numbers. Many mathematicians have contributed since, and today we know of 39 perfect numbers. As you may guess, discoveries of new perfect numbers have become more frequent with the help of computers. The largest one has more than 4 millions digits, and was discovered in 2001. It turns out that all the perfect numbers discovered so far are even. Will we ever discover an odd perfect number? Will we discover an underlining mathematical law that prohibits this? Live and learn!