Sexagesimal

We use the number sixty to count time.

One hour has sixty minutes. One minute has sixty seconds. This way of counting is very old. It began with the Sumerians.

Later, the Babylonians used it too. Sixty is a great number for sharing. You can split sixty into many equal parts. It helps us measure time and shapes. We still use it to find our way today.

It is a very useful way to count.

Imagine you have a large cake. You want to share it with many friends. It is easy to split it into two, three, or six equal parts. This is because the number sixty is very special. It can be divided by many different numbers.

This way of counting is called sexagesimal. It uses sixty as its base. The Sumerians first used it a long time ago. Later, the Babylonians used it too.

Because sixty is so easy to split, it helps with math. It makes working with fractions, or parts of a whole, much simpler. Merchants used it to divide goods fairly.

We still use this system today. We use it to tell time. One hour has sixty minutes. One minute has sixty seconds. We also use it to measure angles in a circle. A circle has 360 degrees. This is just six groups of sixty.

Even in space, this old system helps. Scientists use it to find locations on maps. It is a very helpful tool for our world.

Have you ever wondered why an hour has sixty minutes? This is not a random choice. It comes from a special way of counting called sexagesimal. This system uses sixty as its base instead of ten. Sixty is a very powerful number for math. It is a highly composite number. This means it has many divisors. You can divide sixty evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Because it splits so easily, it makes working with fractions much simpler.

This system works by grouping numbers in ways that make sharing easy. In a sexagesimal system, you can divide a whole into many equal parts. For example, one hour can be split into thirty, twenty, or fifteen minutes. It can even be split into twelve, ten, or six minutes. You can keep splitting it into smaller parts like five, four, three, two, or even one minute. This makes it very useful for dividing goods. Merchants used it long ago to bargain and trade. It helped them divide large amounts of items fairly.

History shows us that this idea is very old. The Sumerians first used sexagesimal in the 3rd millennium BC. Later, the ancient Babylonians passed this system down. They wrote their numbers using cuneiform marks on clay. They used wedge-shaped marks to show units and tens. It was not always a perfect system. Sometimes they mixed different ways of counting in one text. They did not always have a symbol for zero. Later Babylonian writers used a placeholder for zero in the middle of numbers.

Many famous thinkers used these numbers throughout history. In the second century AD, Ptolemy used base 60 for astronomy. He used it to describe the fractional parts of degrees. In the year 1000, Al-Biruni used it to divide the hour into minutes and seconds. By the year 1235, John of Sacrobosco also used this tradition. Even in the late 16th century, mathematicians used sexagesimal multiplication tables. They did this to calculate sines for science.

We still see the sexagesimal system in our lives every day. It is the standard way we measure time. We say an hour has sixty minutes and a minute has sixty seconds. We also use it to measure angles. A full circle has 360 degrees. This is exactly six groups of sixty. We use these same rules for geographic coordinates on maps. It even helps with electronic navigation. This ancient way of counting still helps us find our way around the world.

The sexagesimal system is a numeral system that uses sixty as its base. Most people today use a decimal system, which is based on ten. However, sixty is a highly composite number. This means it has many divisors. The number sixty can be divided evenly by twelve different numbers: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Because it has so many factors, it is very useful for calculating fractions.

To understand how this works, think about how we divide an hour. One hour can be split into many equal parts. You can have 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, or even 1-minute sections. This mathematical advantage makes the system perfect for writing and calculating fractions. In ancient times, this was a huge benefit for merchants. They used sexagesimal math to divide large quantities of goods fairly during trades.

The system was not a pure base-60 system in the way we think of modern math. Ancient Babylonians used a sub-base of ten to write their digits. They used cuneiform, which are wedge-shaped marks made on clay. A single sexagesimal digit was made by adding small marks for units and wider marks for tens. For example, a digit could represent any value up to 59.

Writing these numbers was sometimes complicated because they lacked a consistent zero. For a long time, there was no symbol for zero at all. This meant that the symbol for 1 and the symbol for 60 looked identical. Later Babylonian texts eventually used a placeholder to represent zero. However, they only used this placeholder in the middle of numbers, not at the end.

History shows that the sexagesimal system has deep roots. The Sumerians originated the system in the 3rd millennium BC. The Babylonians later adopted and used it. The system has also appeared in other cultures. For example, the Chinese zodiac uses a sexagenary cycle. This cycle repeats every 60 steps through a sequence of ten stems and twelve branches.

Great scientists have relied on this system for centuries. In the 2nd century AD, Ptolemy used base 60 in his work, the *Almagest*. He used it to express the fractional parts of degrees in astronomy. In the year 1000, Al-Biruni subdivided the hour into minutes, seconds, thirds, and fourths. Later, in the 17th century, European astronomers still used sexagesimal calculations. Even the mathematician Jost Bürgi used sexagesimal multiplication tables to calculate sines.

We still use modified versions of this system every single day. We use it to measure time, where one hour is 60 minutes and one minute is 60 seconds. We also use it for angles and geographic coordinates. A full circle contains 360 degrees, which is six groups of sixty. Each degree contains 60 minutes of arc, and each minute contains 60 arcseconds. This ancient math remains a vital part of modern navigation and science.