Root Calculator

Pythagoras' theorem states that "the square on the hypotenuse equals the sum of the other two squares. It may be derived by any of a large number of methods. Fill in the lengths of any two sides (c being the hypotenuse), and this calc will evaluate the third.

The sum of finite arithmetic and geometric progressions and the sum of an infinite geometric progression are found. Known equations are used to evaluate the sums, so an iterative approach is not required. Infinite geometric series can only be solved if b lies between -1 and 1. Fill in the variables according to the diagram, and the sums will appear. An arithmetic series is solved by adding the first and last terms and then multiplying by half of the number of terms. A geometric series is solved by multiplying the entire sum by b and subtracting the result from the original sum. For example, to add all the numbers from 1 to 100, make a=0, b=1, n=100 (and look at arithmetic series). To calculate z, the input n is not required. Note that in the special case of b=-1, z is undefinable but not infinite.