"Because the actual geoid is so complicated a **reference ellipsoid **is used as a mathematical model for calculation purposes."

So the earth is **not exactly an ellipsoid** (an oblate spheroid), but is **close enough** to one for most purposes.

I do not see any logic in this. If its so complicated that you can't calculate it with real numbers, I am unconvinced!

When was last time that " 2+2 = 4.2 " was accepted as mathematical fact!?

In fact how did the topic turn to pixels??? Do we now base our calculations on photos of earth to prove its shape?

Not acceptable!

**You** "do not see any logic in this. If its so complicated that you can't calculate it with real numbers," **you** are "unconvinced!"

Well, tough cheese, Mr N30! You cannot

**calculate** the shape of the a physical object like the earth,

**you have to measure it!**And nowhere did I say we "now base our calculations on photos of earth to prove its shape"!

In earlier times some relatively small measurement was taken, and extrapolated to

*estimate* the dimensions of the whole earth.

Erosthanes measured a distance and a latitude spacing (from sun elevation) and extrapolated to the whole circumference.

Al Biruni measured the "dip angle"

^{[1]} from a measured altitude to the horizon, used that to calculate the "curvature" and hence the radius. His measurement, done around 1,000 AD, was probably the most accurate measurement till recent times. It was amazingly (and maybe fortuitously) accurate, though he was a meticulous surveyor.

More recently (say from 1,600's on) a baseline would be surveyed in distance and latitude separation, and extrapolated to 360° (basically Erosthanes method). This has been done at various latitudes (from around Newton's time) to find the "ellipticity".

It is only comparatively recently, by using satellites, that more direct and accurate measurements of shape of the Earth have been possibile.

But, you cannot "calculate" the shape of a (very slightly) irregular object like the Earth.

Now it's your turn. Show me

**your** precise

**calculations** for

the circumference of the flat earth,

the circumference at the equator of the flat earth and

the height of the sun.

[1] By the way Al Biruni's dip angle measurement gives the lie to the Flat Earth claim that "the horizon always rises to eye-level". It doesn't.