: How do ancient theorems like Pythagoras’ theorem and Heron’s formula work with the metric system , even though they were invented way before it ?
In: Mathematics
You could test your assumptions by applying the metric system units to your triangle or whatever unit you want. I’m not a math wiz but I’m going to guess that the theorems will hold up to any unit of measurement you want to use. Otherwise, how did any body build anything in any country with some kind of geometry
The theorems were not designed with any unit in mind.
They describe how things relate to each other, regardless of what was actually put in.
A triangle with sides of length a and b, would have a hypotenuse of the squareroot of (a^2 + b^2)
Doesn’t matter whats put in a and b, sides of length 1,5, 19 or 21389879, doesn’t matter if the units are stadia, miles, chinese li, millimeters, microns or kilometers.
The relation ship is all that matters.
Geometric theorems work with ratios. Basically, a 3-4-5 triangle remains the same regardless of if it’s in inches or cubits or meters. This is because as long as the proportions of the sides remain the same, the properties of the triangle do as well.
Math should work with any system of measurement, not just metric!
Imagine you fill up a bunch of water jugs right to the brim, and put them on a kitchen counter.
When you put one jug next to another, you *always* get two full jugs of water, right? Always always always.
And if you decide to make a ‘square’ shape with sides of three jugs of water, you always end up with nine full jugs of water. Always always always.
So here’s the thing – it doesn’t matter if you call those jugs “one litre” or “half a litre” or “forty-five litres” or “two quarts” or “one teaspoon full”.
Your **name** for how much water you end up with will change (the units / system you’re using), but the actual **amount** of water won’t, and more importantly, the **rules of math and logic** that determine that amount of water also don’t change.
They’re more fundamental.
Because they describe the relationships between physical distances and areas. This has nothing to do with the system you use to relate physical characteristics to numbers. I could start a new measurement system based on the length of my favorite nose hair. Both of those theorems would work just fine with it.
Because they are formulas based on ratios not specific digits.
Source: honestly I could be completely wrong, but if I am Reddit will correct me.
They work with **units**.
3^(2) + 4^(2) = 5^(2) whether you are using inches, meters, ångströms, cubits, furlongs, or parsecs.
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