Yeah what a typo. The exact number is : π

I'm procrastinating a bit here so you can skip the rest of the post - unless you're bored too.

It's only when you have to actually draw something that you need to plot in an approximation of π with however many decimals are necessary, and only then depending on the accuracy of your tools.

In a lot of math it pays off to save it for later and eliminate it from the equation on both sides or at least only do it once.

And even then it's futile. In most construction cases, it's probably better to construct the π physically using a compass, even if it means constructing a compass first.

Let's step back. For straight lines, people say "measure twice, cut once", but in reality you also hardly ever need to measure anything in any kind of unit at all. For instance, if you need two boards of equal length, you don't need to make a measurement at all. Just put them on top of each other and saw both pieces at once. They'll be more identical than any attempt to measure and cut both pieces individually. Or if you want all your terrace boards to end neatly, don't even measure them. Just place them all and cut one straight line through the excess at the end. Copying a length of undetermined length is as easy as to place stuff next to each other and cut. "The length of some board" is just as good of a unit as anything else right?

The same kind of ideas also exist for trigonometry, but this might take a little more abstract thinking. Let us make an angle. Instead of measuring or calculating, you just place two sides of your folding ruler against the object and you can copy that exact angle. This can obviously be turned around and create the opposite angle and those kind of tricks.

So let's say we don't know the angle or have anything to copy from at all. Pythagoras is easy to construct. It's as simple as putting stuff up with a 3/4/5 and there's the right 90° angle. Using a compass we can also easily construct 60° or multiples or fractions of it. We do not ever need a specific angle that isn't already a factor in or of 60 or 90. Want the gutters to drain? One end goes above the other. As easy as that. Want two sides to meet? Just lay down a straight line between the two.

Take a look at this which appears to be a mathematical work of wonder. I am willing to bet that they didn't calculate a god damn thing with any amount of digits. It's all made by using a (large) compass or "rig" as it is called when you attach two pieces of wood to make a compass.

Anyway. I don't mean to put down to your skill of memorisation. I admire it, and I can't do that.

If you have any interest in applied trigonometry, I can highly recommend the app: euclidea (android). I honestly think I learned more from playing this game than from any math class I ever took.