Wonderful written. Actually very easy to disprove flat earthers dream world.
The point is either flat earthers are trolling or their sole acting is based on believe and they would never accept a disprove. Means rational arguments don't count, only their believe in such a dream world counts.
This is based on this link:
https://flatearthinsanity.blogspot.co.uk/2016/08/flat-earth-follies-nearby-sun-impossible.html
I've drawn a little sketch. But first a reminder of some simple trig.
In a right angle triangle the tan of an angle, say alpha , tan (alpha) = height / distance. Here visualise a street light of height 5 metres, where we are 5 metres away from the base. The angle from our foot to the top is 45 degree. Alpha is 45 degrees and tan alpha = 5 / 5 =1
If we are 10 metres away tan alpha = 5/10 = 0.5
or 30 metres away then tan alpha = 5/30 = 0.166 recurring
We can rearrange the formula to make height the subject of the formula.
So height = distance from base * tan(alpha)
OK so at 5 metres away NOT KNOWING THE HEIGHT we can calculate it by using 5 * tan(45)
= 5 * 1 = 5 m - we have of course measured the angle with some instrument
At 10 metre away, measuring the angle we then calculate 10 * 5/10 = 10 * 0.5 = 5m
At 30 metres we get 30 * 5/30 = 5m
The height is the same for the top of the lamppost, no matter how far we are away from it. Trivial, but I mention it for the next part....
In the Flat Earth model the Sun is the same distance above the Earth all over:
Starting from the assumption that the Sun is near the Earth - like a lamp post, My picture represents a person at two points at two different latitudes. The far left represent the sun overhead at the equator. The top diagram could be at a hotter latitude where alpha = 80 degrees ,corresponding to a 'round earth' latitude of 10 degrees. The bottom might give a value of alpha of say 30 degrees, corresponding to a latitude of 60 degrees
The link I give, gives the distance from the equator along with the observed angle of the sun for a number of latitudes. All of these are at the same time and incontrovertible. Trivially we could use our phones to speak to other people at different latitudes with measuring devices - sextants, I think they're called.
If our provisional model is correct the lamp post sun should be at the same height as observed from all positions on the plane. I've copied from the link given
Sun At Equinox
Equator (miles)
Is It?
It isn't.
I want to say something about the reason why the flat earth model is being put out there. I believe there are fundamentalist Christians/Jews/Muslims who want to view reality through the lens of their religion rather than through optical instruments. Those promoting flat earth find fertile ground here.
I believe there are another body who do it. They are people who wish to discredit the truth seeking community, who amongst other things will say NASA hoaxed the world. A lot of flat earth you tube videos will demonstrate the falsity of NASAs claim and then started blarhing about a 'Flat Earth' I suggest this is a psi op. I noticed that puppet Obama was going on about 'Flat Earthers' not long before his term came to an end. LOOK out for Trump expressing the same meme.
I'm suggesting the Powers That Be are putting out this 'Flat Earth' meme to discredit rational challenges to explanations of events and paradigms in the world that are being rightly being articulated.