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.
That Euclidea game is pretty neat actually. Too bad your link didn’t and won’t work for me though, I’m not signed into Google, so the Play Store doesn’t work for me.
It’s close enough that you won’t find any difference when using it in any practical sense. However… How do you construct 355/113 practically?
No, if you want to do anything with a circle practically, you use the radius or diameter. That’s how it’s constructed.
In the rare case you’d like to know what the circumference or area of a circle is, your won’t find the fence or paint in those specific sizes anyway, so the rounding is not by decimals, but by arbitrary lengths of fence or buckets of paint.
You must have installed my gutters because while one side is higher than the other, they never considered how level it was, because the fucker never drains completely
I had that same issue. It turns out that my entire house has tilted ever so slightly at some point in the past.
I had the gutters replaced this year, but even the carpenters had difficulties understanding the issue. The boards behind my gutters are sloping inwards in a 45° angle as it was customary to do in the 70s when the roof was changed, so when they moved the gutter downwards they’d also move them inwards, which inevitably resulted in the lower end being too inwards to catch the flow from the roof. Despite several attempts to explain this, it was apparently too difficult to grasp. I’ll see if it works with the summer rains, otherwise I will have to adjust them myself, by inserting incremental increasing sizes off spacers between the boards and the gutter hangers… it won’t be pretty, but at least it’ll be mathematically correct and functional.
![Being courteous [Off the Mark]](https://lemmy.world/pictrs/image/2beb4ee8-a325-46ba-a0e7-1b2b60e84930.jpeg){kind=link}
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.
That Euclidea game is pretty neat actually. Too bad your link didn’t and won’t work for me though, I’m not signed into Google, so the Play Store doesn’t work for me.
But I found it on APKPure Store haha!
Hmm… it works for me when I chose to “open in external” which does pop up the Google play store. I’m not sure of how to link it otherwise.
Anyway, yes it’s pretty neat. I’ve tried other similar apps, but this one is the best in my opinion.
Nah, your link is fine for most Android users. I’ve just chosen to never sign into Google on this particular phone, which comes with consequences.
Play Store and other Google apps don’t work correctly, so I just use alternatives.
Wanna have some approximate PI fun?
355/113
Close enough for government work right?
It’s close enough that you won’t find any difference when using it in any practical sense. However… How do you construct 355/113 practically?
No, if you want to do anything with a circle practically, you use the radius or diameter. That’s how it’s constructed.
In the rare case you’d like to know what the circumference or area of a circle is, your won’t find the fence or paint in those specific sizes anyway, so the rounding is not by decimals, but by arbitrary lengths of fence or buckets of paint.
Wonderful response!
But… how many circular bananas does it take to make a single straight banana?
http://bananaforscale.info/
I’m also saving your comment for later. My nerdy soul thanks you kindly 👍
You must have installed my gutters because while one side is higher than the other, they never considered how level it was, because the fucker never drains completely
I had that same issue. It turns out that my entire house has tilted ever so slightly at some point in the past.
I had the gutters replaced this year, but even the carpenters had difficulties understanding the issue. The boards behind my gutters are sloping inwards in a 45° angle as it was customary to do in the 70s when the roof was changed, so when they moved the gutter downwards they’d also move them inwards, which inevitably resulted in the lower end being too inwards to catch the flow from the roof. Despite several attempts to explain this, it was apparently too difficult to grasp. I’ll see if it works with the summer rains, otherwise I will have to adjust them myself, by inserting incremental increasing sizes off spacers between the boards and the gutter hangers… it won’t be pretty, but at least it’ll be mathematically correct and functional.
Haha I feel the pain