How different number systems, relate to the same thing.

That’s a good question, and is the very foundation of math.

So, I’ll give it to you by relating it to Sine and Cosine. On a right triangle, if the hypotenuse is 1, the other two legs will equal something. And if you make a circle—hang on I’m going somewhere—with the hypotenuse, the legs will be equal to sine and cosine, based on the angle made by the hypotenuse and the cosine leg. So every single degree has a measurement for those numbers—which there’s no algebraic way to deduce, except through maybe pythagorean theorem or analytic geometry, but you also just have to measure it; which may also be what they mean by you can’t do a proof through algebra, except by trial and error

So, that number, which for sine of 60 degrees, the number is √3/2. So, in Roman Numerals or Binary, there will be a way to represent that. But the thing itself, is what the number actually represents.

So, in all things, a number represents a physical object. If Gravity, it’s Gravitational Force; if Mass or Weight; if Quanta; if atomic force or charge in a Chemistry Equation. So, those will represent the same value, based on the context of the equation.

Now a formula, is the next thing to learn. A formula is a shape, that relates to the numbers we measure, and it derives measurements for unknowns through logic, by figuring from what is known, to the unknown. As that’s what a formula is meant to do. A formula is the logic of a shape, so in Trig Functions, the formula is the shape itself, and the sine or cosine or tangent are the numbers we use, to derive information about unknowns. Such as to find area, or other side lengths. Which is highly useful. Because that’s what math is doing, is using known information, and logic, to come to conclusions about unknowns, because the logic of the shapes agree. And through ratios of the object’s similarity, we can augment this, or decrease it, to find new numbers.