How to stake out a square with only cords and a measuring tape |
25
JUN
09
Last week my father ask me to help him building a basement for a party tent in our garden. Its measurement should have been 3 meters long and 3 meters wide. To get started we had to stake out a square. The only tools we had was a measuring tape, 4 stakes and cords. We neither had a goniometer, a pocket calculator, nor some large enough rectangular shape like the outside cladding of the party tent or the exposed-aggregate flagstone that we wanted to use as flooring. Both of which were not delivered at that point. Now how to get to a square? This is what I did:
I plunged the first stake to my liking. The second stake I plunged in a distance of 3 meters from the first. I then attached cords to both stakes. One cord I cut at 3 meters. The other cord I wanted to cut at the length of the squares diagonal. The idea was that when I stretch those cords the only place where their ends would touch would be the position of the third stake. The position of the forth stake I would get by simply switching the attached cords and do the same stretching and touching exercise again.
That was the theory but how in heaven do I get the length of the diagonal of my fancy party tent basement?
As anyone else I suppose I still could remember the infamous Pythagorean theorem which was hammered into my cute brain at that time :): a2 + b2 = c2. What this theorem means viewing at our problem at hand: if you have a rectangular shape and you know the height and width of it, there is a trick to get the length of the diagonal: you simply take the height in the square add the width in the square of that square. The you take the root of that result and voila you have the length of the diagonal.
Example: we have a rectangle with a height of 6 cm and a length of 8 cm. Now according to Pythagoras the length of the diagonal would be the root of 6*6 (36) + 8*8 (64) which would be the root of 100 or 10. As we can see in the figure the Greek was right!
Unfortunately, the numbers weren't that "easy" in my case because 3*3 + 3*3 makes 18, now what is the root of 18? As mentioned above I didn't have a pocket calculator, so I tried to estimate. 16 would be 4 in the square and 25 would be 5 in the square. Thus the root of 18 has to be between 4 and 5. I decided to take square 4.5 to begin with.
The next problem: what is 4.5 times 4.5 without pocket calculator? Quick? Fortunately I already posted how I multiply two two-digit numbers in my head and - flosh - got 20.25. Since 18 lies between 16 and 20.25 I now knew the number I was looking for had to be between 4 and 4.5. At that point I decided that even the grandmaster of mental arithmetic has to know when he gets more real than reality so I made an approximation and took 4.25. (While writing this post I calculated 18.0625 for 4.25 to the square, not bad an approximation isn't it?).
Done! Well not entirely, now the hard work started, I had to scoop out a leveled basement. Fortunately I had a water level to help me at this task :). When we finally placed the flagstones in the basement and the almost perfectly aligned in my square I had the same feeling as Hannibal from the A-Team had at the end of every episode: "I love it when a plan comes together".
