#### American Pythagoras

Figure 1: “Theorem of Pieter Goras” - an aproximation formula

A transformation of a vector to an absolute value is often demanded in radar unit and therefore the application of the law of Pythagoras. Unfortunately, the calculation of the square root is in the assembler or in a mathematical hardware wiring electronic very complicatedly. The problem is, that the calculation of a square root needs different steps depending on the values a and b.

Therefore an approximation formula is used
whose precision is sufficient in most cases, and this procedure provides,
that all possible values of a and b
need the same number of program-steps (i.e.: it needs the same time!):

The sum of the length of the longer side and half the length of the
shorter side is approximately the length of the hypotenuse.

c ≈ a + 0,5 • b