Angular

Angular step

Angular velocity

Y angular velocity

Z angular velocity

So it measures acceleration, angular acceleration

Due to this new error, this new angular error, we don't necessarily trust this number.

We know that if there's no angular error, our circumference that we calculate is 46,250 kilometers.

So it turns out the inertia, which governs angular motion, scales as a fifth power of R.

So as a result, the angular acceleration, denoted by the Greek letter alpha here, goes as 1 over R.

So actually, using this angular error, we can actually explain away why Eratosthenes made the mistake that he did maybe.

We can answer that by noting the fact that the moon has an angular size in the sky of about half a degree.

This means that our angular error, this 1.4 degrees can introduce an error in our calculations, can skew our calculation by as much as 24 .

Something very interesting is going on here in the angular gyrus, because it's the crossroads between hearing, vision and touch, and it became enormous in humans.

We need to go from this angular error to an error in circumference, which means we have to do what's called propagate this error through our calculation.

The last thing I want to talk about before we move on to our next potential source of error is quantifying how much this angular error affected our measurement or our calculated circumference as a percentage.

And by comparing the full angular measure of the circle 360 degrees to this portion α, we will define that if we knew d and we knew α, we can calculate the circumference of the earth.