For the Mathematically Minded: Disproof of FE

A pompous prince pineapple....

Another good 'un

Nice one Roundy, better than you though. I'm having trouble typing

I'm not referring to Uncle Tom

Oh, you're referring to Gulliver? 

Yeah, it applies to him, too, I guess.  He's kind of an ass, isn't he?

Shoots at a fish in a barrel and wants applause....

I doubt he's a donkey but he's an arse alright

then there's petty and pitiful and petulant

P words are fun 

I doubt he's a donkey but he's an arse alright

Oh Gayer, you and your quaint little language. 

Seriously, I love the word "arse".  It actually sounds better than "ass", I think.

remember Eliza Doolittle: "Move your bloomin' arse"

Then use arse more then you silly!

I think I will, now.  It's not exactly a term that gets thrown around often, here.  I'm afraid I would "stick out in the crowd" and "be perceived as different" and that's a scary thought for someone who "likes to just blend in" like me. 

Marlow, I loved that movie.  Not much for old lavish musicals most of the time but that one was hysterical.

This thread is not for everyone (everyone is welcome, but I expect not everyone will be comfortable with the mathematical nature of this proof) but for those with some faith in mathematics I offer this as proof that the Earth is not Flat. I have taken parts of it from my other threads, but I held back on this part because it is not immediately obvious enough to make a super-strong argument (especially vs. the unmathematical babblings of Mr Bishop). Anyway here goes:

I return again to my favourite FE topic: the sun. I like it because we've all seen it, seen it rise and set, and any observations we make are repeatable daily. The FET explanation of the sun's dipping below the horizon is that it is moving away while maintaining a constant altitude, therefore we can take three points O, S and P as the Observer, Sun and Point at which the sun is directly overhead. These form a right angled triangle with the right angle at P and the hypotenuse OS. We must consider also the sun's apparent angle (from the observer's POV) to the horizon as the angle at O which we will call ø.

It may be helpful for you to draw yourself a diagram at this point....

We can see that the distance OP is a function of ø and SP such that:

tan(ø) = SP/OP

Alternatively:

OP = SP/tan(ø)  or   OP = SPcot(ø)

We know SP (the perpendicular distance from sun to ground) is a constant (700 miles, 3000 miles, whatever you like really). OP and ø are variables as the sun moves closer and further, moving towards and away from the horizon (sunrise/sunset).

Time to bring in another fact about the sun: We know it moves through the sky at a constant rate, that is to say, the rate at which ø changes with time is constant. As the sun is moving at constant speed OP is also at a constant rate of change. We can therefore, with a little chain rule, show that:

d/dt(ø) = k  d/dt(OP) = q   therefore  d/dOP(ø) = k/q which is constant.

The problem is, this is a direct contradiction with our earlier statement about the sun, as if OP = SPcot(ø) where SP is constant:

d/dOP(SPcot(ø)) = -SPcosec²(ø)

Which is clearly not constant.

The practical interpretation of this is that while in RE, the sun should (and does) move at constant angular velocity, in FE it should quite clearly vary in angular velocity. Indeed, the rate of motion tends to 0 as ø tends to 0.

So there it is. FEers? Tom if you do try this one, please don't copy paste or say you've answered before. This problem has been stated before, but never demonstrated in such a way. I expect your refutation, if you have one, to be mathematically competent and not dismissive. If there are other FEers who are more mathematical I'm sure you'll have no problem checking this.

As ever, I await your responses eagerly!

Back to the OP, I apologize for getting your excellent thread off track.

the sun. I like it because we've all seen it,

In Britain we see it once every hundred thousand years or so...Then we worship it and get sunburned...

anyway, ignore this post and continue on topic...