Message from @Frolic
Discord ID: 569255692653821953
forget earth
i saw you guys debating how the earth curve is calculated
Why are we forgetting the earth
ok go ahead with earth lol
each section curves the same amount in the pizza its not getting squared
You asked for a formula that works for the whole sphere
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 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
What is the significance of the first being parabolic?
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