Archive for the ‘high-school’ Category

How to solve it

Tuesday, December 15th, 2009

Pyrofessor Polya is not kidding. Consider this: What’s the side of a square inscribed inside a triangle?

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On a cold night, you can hear forever

Sunday, December 6th, 2009

Sound travels faster in warmer air than in cooler air.
Sound travels faster in denser media.
Speed of sound in a gas is almost independent of the density of the gas.

On a cold night, you can hear sound from farther on because of refraction.

Refraction is also why sometimes thunder for faraway lightning goes missing in action.

References:

http://paws.kettering.edu/~drussell/Demos/refract/refract.html

http://www.usatoday.com/weather/resources/basics/sound-refraction.htm

http://en.wikipedia.org/wiki/Speed_of_sound

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The Tautochrone Problem

Sunday, December 6th, 2009

Nature honors us with the mere existence of solutions to problems like the Tautochrone problem (and the fact that it is identical to the solution to the Brachistochrone problem). So dude’s got to give a patient reading to the calculus of variations.

http://en.wikipedia.org/wiki/Tautochrone_curve

http://www.gap-system.org/~history/PrintHT/Brachistochrone.html

Somebody else got a handle on it already, and look how much money he’s saved:

http://www.aticourses.com/enhancing_saturn_v_moon_rocket.htm