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January 11

Perimeter of a trapezium

What is the formular to find the perimeter of a trapezium —Preceding unsigned comment added by 202.170.37.10 (talk) 03:31, 11 January 2010 (UTC)[reply]

What information do you know? Often you know at least two of the four side lengths, and you can usually find the others by using the Pythagorean theorem. —Bkell (talk) 05:33, 11 January 2010 (UTC)[reply]

(Assuming that you mean the shape with two parallel sides, called a trapezoid in the USA) If you know the lengths of the parallel sides, the height, and the two angles at A and B, then the perimeter is just a + b + h(cosecÂ + cosecB).
As Bkell says, for other possibilities, you can often use "Pythagoras" or Trigonometry if you have enough information. (Trivially, if you know the lengths of all four sides, just add them together!) Dbfirs 10:02, 11 January 2010 (UTC)[reply]

Smoothness Scale In Number Theory

Have there been any reasonably good attempts to refine the idea of relative smoothness of numbers? I'm looking for something like a scale that defines powers of 2 as 1 and primes as 0 (or the reverse), something that gives a pretty good--and increasingly better with size--relative smoothness by some reasonable consideration of it. Is the best out there what's essentially already in the smooth number article?Julzes (talk) 14:37, 11 January 2010 (UTC)[reply]