Just curious...

I know that the furthest you can see on a flat plain or out at sea from where you are standing is about 6 miles, which would mean if you looked all the way from left to right, you'd be able to see 12 miles across. But when you're flying at an altitude of 40,000 ft., how many miles across the earths surface can you see then? Once on a trip to Canada from Houston we were flying at 35,000 ft. and the pilot pointed out Amarillo on the left and Okalhoma city on the right. Since it takes about 4 hrs by road at 60 m/h from Oklahoma city to Amarillo staright across on I-40, that would be approx. 240 miles, but we could see about the breadth of Oklahoma city plus vicinity further on each side. Assuming that it's about 30 miles across and adding the breadth of the Oklahoma city and vicinity and Amarillo, I estimate that we could see at least 300 miles across from end to end, but I can't be sure. Fyling to Cairo at 39,000 ft over Italy, from what i could make out of the land below, we could see 200 miles across to the right of the plane (where I was sitting) and coming to Cairo at 40,000 ft, Flying over Saudi and the Red Sea, I estimated the distance to be approx. 200 miles as well, meaning we should be able to see approx. 400 miles across. I wonder if I'm any where close to being right. It's not important, but I'm just curious...