objections to the roundness of Earth

[bilby]

https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf

Sets out the simple case in an easy to understand format.

 

[Loren Pechtel]

And the point is?

The point is that the earth doesn't really look flat. It is only the irregularities, the unsmoothness, plus our closeness to the ground, that hides the curvature.

Consider the mountain picture earlier. That shows what's really going on--our ability to actually see far enough to see the curvature is limited.

A while back I found a site that you click a point, it shows you what you should be able to see. Somewhat mistaken, a point put on top of the highest point in the area was wildly wrong but a point nearby was pretty close to accurate except for not understanding that some land to the south is shadowed. But there's a major difference between what it showed and what I could see--all of the more distant lands were completely blanked by the atmosphere. Supposedly I have line of sight to some points ~300 miles away--but the best I have actually been able to do is perhaps 100.

 

[Loren Pechtel]

Flat earth is the stupidest conspiracy theory I’ve ever seen as it is nearly trivially debunked by almost anyone anywhere.

What portion of Flat-Earthers actually believe the Earth is flat? Aren't many just having fun?

I'm guessing that VERY few people agree that Birds aren't real.

Just like God. Real unless defined integer. Just ask any Fortran programmer.

 

[lpetrich]

By the well known Quasi Conformal Mapping Jackson-Jones-Smith-Rodriguez theorem spherical is a special case of flat.

Source?

One can do a coordinate projection from a spherical surface to a planar one, but that projection will inevitably cause some distortion. One can do a projection that preserves some property, but it will be at the expense of sacrificing other properties.

Spherical coordinates: radius r, colatitude (90d-latitude) or polar angle ap, longitude or azimuthal angle az:
r*sin(ap)*cos(az), r*sin(ap)*sin(az), r*cos(ap)

Rectangular coordinates: x, y, polar coordinates: r, a:
x = r*cos(a), y = r*sin(a)
r = sqrt(x^2+y^2), a = arctan(y/x)

Kinds of projections:

• Rectangular: x = az, y = Y(ap)
• Polar: r = R(ap), a = az
• Quasi-rectangular: x = X(ap)*az, y = Y(ap)
• Various others

 

[lpetrich]

Examples:

Polar:

• Distance-preserving for some point: R(ap) = ap (the UN-flag projection)
• Orthographic (view from a distance): R(ap) = sin(ap)
• Equal-area: R(ap) = 2*sin(ap/2)
• Stereographic (conformal): R(ap) = 2*tan(ap/2)
• Modified stereeographic: r = rsg^p, a = p*asg for some parameter p
• Gnomonic (geodesic-preserving): R(ap) = tan(ap)

Will use al = pi/2 - ap for these ones:

Rectangular:

• Same-latitude: Y(ap) = al
• Equal-area: Y(ap) = sin(al)
• Mercator (conformal): Y(ap) = log(tan(pi/4 + al/2))

Quasi-rectangular:

• Same-latitude equal area: X(ap) = cos(al), Y(ap) = al
• Mollweide (elliptical boundary): X(ap) = cos(ax), Y(ap) = (pi/2)*sin(ax) where ax - sin(ax)*cos(ax) = (pi/2)*sin(al)

 

[steve_bank]

Source? A joke.

Science and math are definitions. There is no real debate in my option. Somehow fits a definition or it does not. If no existing definition fist create a new definition.

Roundness is more metaphysics than math or science. In Geometric Dimensioning and Tolerancing used in mechanical engineering to specify shoes of parts, roundness has a definition, as does flatness.

We went through this before. There are models for the Earth. Spherical as a simple model accurate enough for mnay misapplications.

Geometric dimensioning and tolerancing - Wikipedia

en.wikipedia.org

If I were to be technical using a mathematically perfect sphere as a model I would say something like the Earth is spherical to +- xx meters referenced from the center of mass of the Earth.

A 3d topological model would have distance from center to surface vs latitude and longitude.

There are flat 2d maps that show distance and relative position. There are topological maps with altitude contours.

As to the OP question, as humans do not have appeared to have changed much I word think the ancient arguments for and against a spherical Earth would have been no different than debates today.

Creationism vs evolution. Natural vs human caused climate change.

I read a short book on topology and conformal mapping years ago for general background information. It has practical uses.