www.radartutorial.eu Radar Basics

American Pythagoras

Theorem of Pieter Goras

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

A transformation of a vector to an absolute value is often demanded in a 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