Message from @AstralSentient
Discord ID: 569256091754561546
i still dont think the formula involved squaring anything
b/c that's an approximation of the proper formulat
only valid over a certain distance
It's just a simpler formula
Surveyors use it
literally i hired a surveyor to come survey my property he was a freemason so is my dentist
im not saying its a big conspiracy lol
just they were free masons thats all
So do you understand the equations now
no
I'll summarize
h is amount of curve, d is distance away from where you start
h=8*d^2 is one equation
h=R[1-cos(d/R)] is another equation
the 2nd is more accurate
the first is good for several hundred miles
the first is a parabola, the 2nd is a circl
the 2nd is more accurate
the first is close, for small values of d
si the second on exponential
a parabola is not a circle, thus it can't be used to accurately represent a circle
ok is the second formula exponential
Why not?
@AstralSentient well it is accurate 'enough' over the short distances, but it doesn't match a circle, it's a different shape
no more than a zigzag represents a straight line
I'm not quite sure of the context. You mean parabola on a graph with horizontal distance and vertical drop as your inputs or just that the tangent line from the curve giving h= 8d^2 makes a parabola?
both of what you said are teh same thing
No they aren't, one is a visual example, another is a coordinate plane graph
Both the same
8d^2 is a parabola
and only matches a circle for a limited range of d
They aren't the same. I think that is your mistake here. Assuming they are the same.
Another important thing to consider is that height and distance can be different on a sphere. Think of height relative to the center and straight down to the curve from a tangent line.
we're only concerned with the latter height
that's what these equations calculate
and since they're different equations, they give slightly different shapes
one a parabola, one a circle
the one that is a circle is better to use when considering a spherical object like the earth
🤔
Sure, on a graph, with the parabola modeling the drop on a sphere from a tangent line