# What 3 Words

Every so often you come across a product or application that captures your imagination and gets people talking. Imagine this, the next time someone asks you where you live; you don’t have to tell them a post code or a grid reference. All you need is to have 3 key words to hand. What 3 words you may be asking? … Well the 3 words that describe the 3 meter by 3 meter block that could pinpoint your exact location on the surface of planet earth. This new idea developed claims to be far more accurate than a postal address and it’s much easier to remember, use and share than a set of coordinates. Interested? You can try it out here http://what3words.com

So the next time you want to visit your favourite spot on the beach you can easily remember it by having an exact reference for its precise location http://w3w.co/broken.waters.pools ; just make sure you remember the words. The look on your kid’s face when you shout out “Come on kids, we’re off to our favourite spot at broken water pools!” could be etched in the memory for ever.

So that got some of us in the office talking. How many words would need to be able to map the entire surface of planet earth with 3 meter by 3 meter grid? Are there enough words? Could we make a smaller grid? etc…

This called for a little number crunching and some unit conversions. What better tool to pick and start cranking the numbers than PTC Mathcad? First I defined some units for those larger numbers we could expect to come across in such our calculations.

Next, we have the basic calculations that tell us the number of blocks that are required to cover the entire earth in a 3 meter by 3 meter grid.

Using one of PTC Mathcad’s many built-in mathematical functions I can calculate all of the permutations of 3 words with available (current) words in the Oxford English dictionary. Although it’s quite difficult to get an exact number it is stated that the 2nd edition of the 20-volume Oxford English Dictionary contains full entries for 171,476 words in current use[i]. Using that assumption we come up with an impressive number of permutations.

There are clearly more than enough words available to be able to describe the entire surface of the earth with any 3 word combination that represents a 3 meter by 3 meter grid. So how about creating such a grid on the surface of all planets of the solar system. Turns out, we don’t have quite enough and would need many more words in the English dictionary to make that happen.

A further question that came up was, how small a grid size could we create on earth if we used all 171,476 words in the current English dictionary? To answer this question we can set up a system of equations/constraints and by using a PTC Mathcad solve block we are able to solve for the for the exact grid size. We can conclude that there are enough words to create a 3 word reference for a grid size as small as ~ 1 ft x 1 ft. Small enough to define the personal space you occupy!

So if you have an inquisitive mind and want quick answers to your questions, then PTC Mathcad could be that tool to empower you with that ability to answer those questions quickly without needing to be an expert in the product.

If you are interested the worksheet is posted here.