Author Archive
Some stubborn problems associated with the number 3/2
Posted by: Gary Ernest Davis on: December 4, 2010
Fractional parts of powers of The powers of increase exponentially: However, if we keep only the fractional part of – that is, – quite a different picture results: The first few of these numbers are 1/2, 1/4, 3/8, 1/16, 19/32, 25/64, 11/128, 161/256, 227/512, 681/1024, 1019/2048, 3057/4096. Despite much study, there are things about this […]
Why, exactly, is the square root of 2 not a rational number?
Posted by: Gary Ernest Davis on: December 3, 2010
Right angled triangles and The Pythagorean theorem tells us that a square erected on the hypotenuse of a right-angled triangle will have an are equal to the sum of the areas of squares erected on the other two sides: In particular, a right-angled triangle with the two sides adjacent to the right angle having length […]
