The earth is flat not spherical

"I have shown clearly that you would descend at an incredible speed, and this math has not been proved wrong. My opponent appears to be making this angle up." Unfortunately, though the instigator makes this claim, he ignores the fact that he is wrong. I have showed that it is impossible for his numbers to be true, and for two reasons: 1. They do not match up with simple trigonometry. 2. Uses a method which does not work after a certain distance. The descent would have been less than a tenth of what the instigator had suggested; and here's a detailed explanation why: The earth's circumference is about 40,000 km, and is 360 degrees round ( because the arc would be a circle). If I take a certain part of the arc, then the ratio between the part and the degrees from the center would have to be directly related to one another; or in other words, if I take a 400 km path across the surface, my angle would have changed by 3.6 degrees. Assuming that a plane travels at 500 mp/h (804 km), it would take it one hour to change its angle by 7.23 degrees, which translates to 0.12 degrees in a minute, which is a margin of a turn, not noticeable by anyone in the plane. Moreover, keep in mind that the plane isn't rotating in comparison to the horizon, as in order to maintain the same height, it has to keep it's vector of speed parallel to the horizon. I will not address this subject any further, because it has become both irrelevant and useless in relation to the topic. 1. Flight paths. I have already refuted this point quite soundly, so if the instigator has anything useful to add to the table, then he is welcome to. But in order to not seem as though I am running away from the subject, I will yet again quote what I have said in my rebuttal: " The flight stops at a major city most likely to drop off/pick up other passengers, which will spare the company both time, available planes, and money.-" Even if the flight would take longer. Heck, he hasn't yet shown me an example of a non-stop flight taking an oblique path which makes more sense on the flat-earth model; and because the example I have brought is both non-stop and makes more sense on the round-earth model, both the facts brought by the instigator and the facts brought by me fit in line perfectly with MY model, not his. Think of it like this; if it would cost you 1,000 X's of resource to fly a plane from Australia to NYC, and then 1,000 X's of resource to fly a plane from NYC to Chile; or alternatively, 1,500 X's of resource to fly a plane directly from Australia to Chile, yet you still had to fly a plane from NYC to Chile, at the cost of 1,000 X's; you'd rather fly the plane in the first option, especially considering the fact that there aren't many people flying from Australia to Chile, making it less profitable as well. 2. Distances sighted. I find it sad that a well-spoken and probably somewhat intellectual person prefers to be so willingly ignorant. "A slight distortion is expected through 60 miles of atmosphere." The distortion happened precisely at evening, proving the superior mirage explanation to an even further degree. The reason to this is because the superior mirage happens only when there is a difference between the temperatures in the layers of air, meaning that the mirage cannot happen at night. All the sources brought here are taken at daytime, VISIBLY at a hot day, with not even one exception. If you could bring me a case of long distances sighted, deep into the night, and at sea-level, then I would address the point further. 3. Reflections on water. "The fact that waves exist on a flat surface of water has nothing to do with the overall flatness of the surface." What the waves mean is that you have all different angles of reflection, which means that even if the earth was only ten miles wide, you could still see a path of light. Heck, your sheet of metal example only works if you bend the sheet not to a flat surface, but to a CONCAVE. I rest my case. 4. Shifting the burden of proof. I will conclude this round with what is probably the strongest piece of evidence for a round earth that exists. The only possible means of navigation, especially on the long term, is spherical geometry. If you were to use euclidean geometry, you would find yourself lost beyond any degree, proving that the earth is a sphere. CITATIONS: http://www.science4all.org... (at "Why Euclidean Geometry is insufficient") http://www.goodsamt.com... mskilgard.weebly.com/uploads/1/3/8/2/13828679/spheregeo_short.pptx http://www.math.niu.edu... And so on, and so forth.