Happy Pi. Day.

March 14, 2019  - By

In honor of 3.14.2019.

Here is what GPS World’s Innovation column editor Richard Langley wrote about π in an article (“A Sideways Look at How the Global Positioning System Works”) 9 years ago:

3.1415926…. π. Every nerd’s favorite number. It is the ratio of a circle’s circumference to its diameter in conventional or Euclidean space. We use it, for example, to convert angles measured in radians to degrees (π radians = 180 degrees). π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. But we sometimes use an easily remembered fraction, such as 22/7, to get an approximate value. In this case, 3.14. But, if we compute more digits with this fraction, we get 3.1428571…, clearly an incorrect result. A better way to remember π to eight digits is to count the number of letters in each word of the mnemonic “May I have a large container of coffee?”

In computations related to GPS, how many digits of π should be used? It depends. If you are developing your own algorithms and software for modeling GPS observations or determining precise orbits for the satellites, you’ll likely need π to 16 digits for double-precision floating-point calculations. But it would be a mistake to use π to this precision in computing the position of a satellite from the broadcast ephemeris. The GPS interface specification document, IS-GPS-200, specifies a 14-digit value for π (3.1415926535898) in the satellite coordinate computation. Use fewer or more digits, and the resulting satellite coordinates will not be as accurate.

Full article here.

Thank you, Dr. Langley.

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