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Bed sheet Problem

Bed Sheet Problem  You have insomnia one night and decide to remove your bed sheet, which is only about 0.4 millimeter thick. You fold it up once. and it becomes 0.8 mm thick. How many times do you fold it if you want to make the bed sheet thickness equal to the distance between the Earth and the moon? The remarkable answer is that if you fold your sheet only 40 times. then you will sleep on the moon! In another version of the problem. you are handed a sheet of paper with a typical thickness of 0.1 millimeter. IT you could fold it 51 times. the stack would reach further than the sun! Alas. it is not physically possible to create many folds in physical objects like these. The prevailing wisdom throughout much of the 1900s was that a sheet of real paper could not be folded in half more than 7 or 8 times. even if the starting paper sheet was large. However. in 2002. high school student Britney Gallivan shocked the world by folding a sheet in half an unexpected 12 times. In 2001. Galli...

Pyhtogorean Theorams of Traingles

Baudhayana (c. 800 B.c.), Pythagoras of Samos (c. 580 B.C.-c. 500 B.c.) Today, young children sometimes first hear of the famous Pythagorean theorem from the mouth of the Scarecrow, when he finally gets a brain in MGM's 1939 film version of The Wizard o{Oz. Alas, the Scarecrow's recitation of the famous theorem is completely wrong! The Pythagorean theorem states that for any right triangle, the square of the hypotenuse length c is equaI to the sum of the squares on the two (shorter) "leg" lengths a and b-which is written as a 2 + b2 = c2 The theorem has more published proofs than any other, and Elisha Scott Loomis's book Pythagorean Proposition contains 367 proofs. Pythagorean triangles (PTs) are right triangles with integer sides. The "3-4-5" PT-with legs oflengths 3 and 4, and a hypotenuse oflength 5- is the only PT with three sides as consecutive numbers and the only triangle with integer sides, the sum of whose sides (12) is equal to double its area ...