Over five thousand years ago, the Sumerians in the area now known as southern Iraq appear to have been the first to develop a penchant for the numbers 12, 24, 60 and 360.

It is easy to see why. 12 is the first number that is evenly divisible by six smaller numbers:

12 = 1×12, 2×6, 3×4 .

24 is the first number that is evenly divisible by eight smaller numbers:

24 = 1×24, 2×12, 3×8, 4×6 .

60 is the first number than is evenly divisible by twelve smaller numbers:

60 = 1×60, 2×30, 3×20, 4×15, 5×12, 6×10 .

And 360 is the first number that is evenly divisible by twenty-four smaller numbers:

360 = 1×360, 2×180, 3×120, 4×90, 5×72, 6×60, 8×45, 9×40, 10×36, 12×30, 15×24, 18×20 .

And 360 in a happy coincidence is just 1.4% short of the number of days in a year.

We have 12 hours in the morning, 12 hours in the evening.

We have 24 hours in a day.

We have 60 seconds in a minute, and 60 minutes in an hour.

We have 60 arcseconds in an arcminute, 60 arcminutes in a degree, and 360 degrees in a circle.

The current equatorial coordinates for the star Vega are

α_{2019.1} = 18^{h} 37^{m} 33^{s}

δ_{2019.1} = +38° 47′ 58″

Due to precession, the right ascension (α) of Vega is currently increasing by 1^{s} (one second of time) every 37 days, and its declination (δ) is currently decreasing by 1″ (one arcsecond) every 5 days.

With right ascension, the 360° in a circle is divided into 24 hours, therefore 1^{h} is equal to (360°/24^{h}) = 15°. Since there are 60 minutes in an hour and 60 seconds in a minute, and 60 arcminutes in a degree and 60 arcseconds in an arcminute, it follows that 1^{m} = 15′ and 1^{s} = 15″.

Increasingly, you will see right ascension and declination given in decimal, rather than sexagesimal, units. For Vega, currently, this would be

α_{2019.1} = 18.62583^{h}

δ_{2019.1} = +38.7994°

Or, both in degrees

α_{2019.1} = 279.3875°

δ_{2019.1} = +38.7994°

Or even radians

α_{2019.1} = 4.876232 rad

δ_{2019.1} = 0.677178 rad

Even though the latter three forms lend themselves well to computation, I still prefer the old sexagesimal form for “display” purposes, and when entering coordinates for “go to” at the telescope.

There is something aesthetically appealing about three sets of two-digit numbers, and, I think, this form is more easily remembered from one moment to the next.

For the same reason, we still use the sexagesimal form for timekeeping. For example, as I write this the current time is 12:25:14 a.m. which is a more attractive (and memorable) way to write the time than saying it is 12.4206 a.m. (unless you are doing computations).

That’s quite an achievement, developing something that is still in common use 5,000 years later.

Thank the Sumerians!