How did Mayans measure length of the year with precision of 0.00001 days?

Answer 1

Here's an idea:

-- Find two trees that stand outside the opening of a cave that opens to the south.

-- Tape up a piece of cardboard between two trees, with its flat side facing south.

-- Stick a pencil point or a fox tooth through it, to make a tiny hole in it.

-- Back inside the cave, where it's dark, you'll see a dim but nice-sized image of the sun creeping along the rock. Watch it for a few days to learn its motions.

-- Take a bucket of white-mud into the cave, and paint a big area around where the sun's image usually is around noon.

-- Later, after the paint is dry, in the late morning on any day you choose, take a stick with a burned end into the cave, and make a sharp mark on the paint, right exactly at the edge of the sun's image, at any time around noon.

-- From years of watching the sky at night, you already know that the year is 365 days and a fraction. You only need to measure the fraction.

-- Come back to the cave on the 365th day. With the help of everybody in the village, it's easy to count.

-- If the cave wall is 100 feet from the cardboard, then the sun's image is a good 10 inches across, and it's moving 5-1/4 inches a minute, so it's easy to tell when it's right on the mark.

-- The length of time between the (time of day when you made the mark) and the (time of day when the image returns to the mark) is the fraction of a day that the year exceeds 365 complete days.

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I just read through this, and realized that it's garbage and it doesn't work ... at least not in one year. They'd have to do it for several many years in order to pin down the fraction. But I had so much fun writing it that I'm just going to leave it here for you to think about, until the category supervisor comes along and sends it to the circular file. I just hope he gives me a trust point for effort while he's trashing it.