The tallest structure in the world, the Burj Khalifa tower which is 2,722 feet tall. During the Islamic holiday of Ramadan you are not allowed to eat a meal while the sun is up. For those who live in the tower, anyone at around the 80th floor are urged to wait an additional 2 minutes longer than those on the ground floor as the sun is still visible. On the 150th floor that number becomes 3 minutes. This shows that the Earth is round as the sun sets for objects on the ground before those higher up. The same thing happens for sun rise and you may have even seen this effect.
Now for the math. For the Earth, just as you say the curve is 8 in per mile squared, this comes from the radius of 3959 miles which gives a circumference of 24,875 miles. Circumference = 2piradius. This number can vary +/- a few miles depending on who you talk to but it doesn't change the end value when you account for this small error. So to prove the curve we take the height of the tower above Earth which is 2722 feet and find the horizon distance because this is where we agree the sun is no longer visible. If we draw a circle and give it the radius of earth, it will have the curvature of the planet. if we draw a 2722 foot line on the circle we can use that to find the horizon distance. This website may help with the diagram but I will use my own calculations to double check the number it gives http://www.ringbell.co.uk/info/hdist.htm . So with the Earths radius plus the tower in feet on one side and the Earths radius on the other we can calculate the distance from the horizon in a straight line. I get 20902231.64 feet for the radius of earth using 6,371,000 meters as the average radius of earth. so a triangle with c^2 = a^2 + b^2 we get (20904953.64^2) radius plus tower = (20902232.64^2) + b^2. Which gives a value for b = 337341.31 feet or 63.89 miles. So at top the tower the horizon is 63.89 miles away from the horizon. If we can agree on that number, and use the same equation to get the horizon for someone who is 6 feet tall we can see how much the earth has curved mathematically. So (20902238.64^2) 6ft plus radius = (20902231.64^2) + b^2 where b must equal 16660.8 feet or 3.155 miles. Now we can see if it matches the 8 inches per mile squared. So since we know we rotate at 24 hrs, for the time difference of 3 minutes earth would rotate 3minutes / 24 hours or 1440 minutes this means 3 minutes is .00208333333 of one day. One day is one revolution so 2 pi radians / 1440 minutes is how many radians we rotate in one minute 0.004362 radians/minute. Therefore in 3 minutes we move 0.013086 radians of a full circle or 0.7497725707 degrees. Since Arc length of a circle, which is a section of the circumference is equal to the angle/360 * radius we get 43533.11 feet or 8.245 miles is the distance on the surface of earth between someones horizon at the top of the tower from someone on the bottom of the tower. This 8.245 miles is the distance between two locations on earth that see the sun set 3 minutes apart if you were exactly on the ground and exactly on the same latitude.
The sun's light hits the Earth at a tangent on the horizon at sunset by definition. Using the 8.245 miles of Earth rotating in 3 minutes and your number of 8 in per mile we get 65.96 inches. This is the side of a triangle which connects a line tangential to the curve of the Earth from a person on the ground, to a line tangential to the curve of the Earth at the top of the Burj Tower. These lines mark the farthest point a person can see at sea level from the height they are at, which is their horizon. I only used geometry and math to get this far. Extending those tangent lines makes a right triangle
Using the Triangle we just made, we can check to see if the Distances we calculated before are the same as the distances. The sides of the Triangle are the height of the tower minus the 6ft man as "c", the distance to horizon from the top as "a" and the distance from the 6ft man to the horizon as "b". This should be proportional to the Triangle we just made with the side 65.96 inches due to the drop of earth.

This is what we have so far.

The ratio of 2716ft to 65.96 inches is 41.176 ft/inch drop. Any two proportional triangles will have proportional sides. I urge you to test this out on your own. Every minute we rotate, the horizon moves 8.425miles/3 minutes = 2.75 miles which would be 21.99 inches of curved Earth. That means that every minute we would expect that the sun set will rise 905.3 feet above your head. Test this out. Go to a tall building or mountain or anything you know the height of, and at the very moment on an unobstructed horizon you cannot see the sun, start a timer. Time how long it takes for the sun to set on the tall object near you, and use 41.176ft/inch drop or 905.3 feet per minute to see if it coincides with the height of the object. You could even do it in your house if you wanted. Start outside and run up to the top floor or roof with the timer running and see when you cant see the sun anymore. Leave some room for error of course but it should be rather close. This mathematically proves that the 8 inch per mile number is correct. Please try it in a few different spots. Try 5 and see for your self.

Not that I enjoy Islam as I think it is a barbaric and horrible religion, but I know they take it seriously. They do observe Ramadan later at the top than the bottom.