# Pythagoras¶

The ancient Greek mathematician Pythagoras is famous for the invariant of right angle triangles:

$h ^ 2 = w^ 2 + a^2$

where h is the hypotenuse, w is the width of the base, and a is the altitute.

We can calculate the hypotenuse in Felix like this:

fun hypot (w:double, a:double) : double =>
sqrt (w^2 + a^2)
;

println$hypot (3.0, 4.0);  The type double is a standard double precision floating point real number. The sqrt function is in the library, and calculates the square root of a double precision number. The operator ^ denotes exponentiation, in this case we are squaring, or muliplying the argument by itself twice, the literal 2 is a value of type int, a type of small integers. Of course, the operator + is addition. The fun binder is used here to define a function. Then we give the function name we want to use, in this case hypot. Then, in paranthesis we give a comma separated list of parameter specifications. Each specification is the name of the parameter, followed by its type. It is good practice, but not required, to follow the parameters with : and the return type of the function. Then the => symbol is used to begin the formula defining the function in terms of the parameters. The function can be used by applying it to an argument of the correct type, in this case a pair, or tuple, of two numbers of type double. The println is then called on the application using the application operator$.