--- title: "The Maths of Time: Why Clocks Aren’t as Simple as They Look" description: Discover the surprising maths behind timekeeping — from Babylonian base-60 and leap years to time zones, longitude, and the atomic second. Clocks aren’t as simple as they look! image: https://mathsthatclicks.net/hubfs/clock.png --- [![logo for mathsthatclicks.net](https://mathsthatclicks.net/hs-fs/hubfs/Illustration5_smaller.png?width=1778&height=1647&name=Illustration5_smaller.png "logo for mathsthatclicks.net")](https://mathsthatclicks.net) - [Tutoring](https://mathsthatclicks.net/#tutor) - [About](https://mathsthatclicks.net#about) - [Contact](https://mathsthatclicks.net/#contact) - [Testimonials](https://mathsthatclicks.net/#testimonials) - [FAQ](https://mathsthatclicks.net/#FAQ) - [Blog](https://mathsthatclicks.net/blog) - [Resources](https://mathsthatclicks.net/resources) - [Tutoring](https://mathsthatclicks.net/#tutor) - [About](https://mathsthatclicks.net#about) - [Contact](https://mathsthatclicks.net/#contact) - [Testimonials](https://mathsthatclicks.net/#testimonials) - [FAQ](https://mathsthatclicks.net/#FAQ) - [Blog](https://mathsthatclicks.net/blog) - [Resources](https://mathsthatclicks.net/resources) [measurement & geometry](https://mathsthatclicks.net/blog/tag/measurement-geometry) [making connections](https://mathsthatclicks.net/blog/tag/making-connections) [fun maths](https://mathsthatclicks.net/blog/tag/fun-maths) # The Maths of Time: Why Clocks Aren’t as Simple as They Look [![Mark](https://mathsthatclicks.net/hs-fs/hubfs/Mark-250x250.png?width=50&height=50&name=Mark-250x250.png)](https://mathsthatclicks.net/blog/author/mark) [Mark](https://mathsthatclicks.net/blog/author/mark) 11 October, 2025 ![](https://mathsthatclicks.net/hubfs/clock.png)   Have you ever stared at the clock and wondered why it’s divided into 60s instead of 100s? Recently I was looking at some different aspects of time with a couple of different groups of students - looking at time zones and the 24 hour clock with a younger group, and latitude and longitude with a year 11 student.   It made me realise that  I had some vague ideas which I always repeated (*i.e.* the Babylonians loved 60), but had never tried putting together a coherent summary of history of measuring the time.  So now, it was time for some reading... We check the time dozens of times a day, but have you ever stopped to wonder: *why do clocks work the way they do?* The answers are buried deep in history — and they’re surprisingly mathematical. --- ### **Why 60?** Ever wondered why we chop up hours and minutes into 60s instead of something simpler, like 10 or 100? The answer goes back over 4,000 years to the **Babylonians**¹. The Babylonians used a number system based on **60** (what we now call *sexagesimal*). To them, 60 was a dream number: it has more divisors than almost any smaller number. You can split it into halves, thirds, quarters, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths… the list goes on. It’s like the Swiss Army knife of numbers². This flexibility was perfect for **astronomy**. When you’re trying to divide the sky or a circle into equal parts, a base-60 system makes the fractions neat and clean. For example: - 1/2 of 60 = 30 - 1/3 of 60 = 20 - 1/4 of 60 = 15 - 1/5 of 60 = 12 - 1/6 of 60 = 10 All nice whole numbers. Compare that to a decimal system: 1/3 of 10 = 3.333… forever! Messy. The Babylonians also noticed that a year is roughly **360 days**³. They imagined the Sun moving through a giant circle in the sky, one degree per day. Dividing that circle into **360°** was a natural fit — and conveniently, 360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18… making calculations much easier. Base 60 and 360° go hand in hand: fractions of the circle were simple, and so were fractions of time². So every time you say “just a minute,” you’re echoing a decision made thousands of years ago by astronomers looking up at the stars, choosing numbers that made their maths easier. --- ### **The Leap Year Trick** While the Babylonians shaped how we measure hours and minutes, later astronomers had to tackle a new problem,  keeping years in sync with the Sun. We like to say a year has 365 days… but it doesn’t. The Earth takes about 365.2422 days to go around the Sun. That tiny extra 0.2422 adds up! If we didn’t sneak in a leap year every 4 years, our calendars would slowly drift — and after a century, summer would start in autumn. (Not great for beach holidays!) ### Longitude and Time Zones Here’s a neat connection: the Earth spins 360° in 24 hours. Divide 360 by 24 and you get 15° — which is why every time zone is roughly 15° of longitude wide. Noon in London is midnight in Sydney, not because of magic, but because of maths. The Earth is divided into 24 time zones, each roughly 15° of longitude apart. This division stems from Earth's 360° rotation over 24 hours, meaning it rotates 15° every hour. Therefore, each time zone corresponds to one hour's difference in local time. For instance, when it's 12:00 PM in Sydney (UTC+10), it's 10:00 AM in Perth (UTC+8). Understanding time zones is more than just knowing when it's morning in New York or night in Tokyo. It’s about applying mathematical concepts to real-world scenarios—a key focus in the NSW Year 11 Standard Mathematics syllabus. #### Latitude, Longitude, and Time Calculations The syllabus emphasizes using latitude and longitude to determine time differences. By calculating the longitudinal difference between two locations and applying the 15° per hour rule, students can determine the time difference between those locations. For example, if two cities are 45° apart in longitude, the time difference is 3 hours (45° ÷ 15° per hour). #### Practical Applications in the Syllabus The syllabus includes practical problems involving: - **Coordinated Universal Time (UTC):** Understanding UTC as the baseline for timekeeping and how local times are offset from UTC. - **International Date Line (IDL):** Recognizing how crossing the IDL affects the calendar date, which is crucial for international travel and communication. - **Australian Time Zones:** Applying knowledge of Australia's three main time zones—Australian Eastern Standard Time (AEST), Australian Central Standard Time (ACST), and Australian Western Standard Time (AWST)—to solve real-world problems. These topics are part of the "Working with Time" unit (MS-M2) and help students develop practical skills in time calculations, enhancing their understanding of global timekeeping systems⁴.   --- ### **The Quest for the Perfect Second** Historically, a second was defined as **1/86,400 of a mean solar day**, derived from dividing the 24-hour day into hours, minutes, and seconds¹. However, the Earth’s rotation is not perfectly uniform; it fluctuates slightly due to tidal friction, seismic activity, and other geophysical factors. This made the solar-day definition of a second increasingly inadequate for scientific and technological purposes. In 1967, the **International System of Units (SI)** redefined the second based on a property of the cesium-133 atom. The official definition became: \*“the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom”\*². This atomic definition allows time to be measured with extraordinary precision, to the level of billionths of a second, and forms the basis for modern technologies such as GPS, telecommunications, and high-speed data networks. By moving from an astronomical to an atomic standard, scientists ensured that the second is **consistent, reproducible, and independent of irregularities in Earth’s rotation**. --- ### **Final Thought** Exploring these ideas with students reminded me that time isn’t just a measurement, it’s a story of human ingenuity. Every clock in our classroom is a link to thousands of years of maths and curiosity. Time isn’t just about watches and calendars — it’s an ancient puzzle, solved with fractions, geometry, astronomy, and now physics     --- **Sidebar: The Babylonian Zodiac** The Babylonians didn’t just give us base 60 — they also carved up the heavens. Around 500 BCE, they divided the sky into **12 equal 30° sections**, tracing the Sun’s path across the stars³. They gave each section a name, like *The Heavenly Bull* (Taurus), *The Great Twins* (Gemini), *The Lion* (Leo), and *The Scales* (Libra)⁵. Later, the Greeks borrowed this system, swapped in their own myths, and handed us the zodiac we know today. So the same maths that gave us **60 minutes in an hour** also gave us **12 signs of the zodiac**. Two legacies of Babylonian sky-watching, still ticking away in our modern world. --- ### References 1. Wikipedia. (n.d.-a). *Sexagesimal*. https://en.wikipedia.org/wiki/Sexagesimal 2. Northern Kentucky University. (n.d.). *The Babylonian number system*. https://www.nku.edu/~longa/classes/2014fall/mat115/mat115-006/images/babylonian/BabylonianNumbers.pdf 3. Wikipedia. (n.d.-b). *Babylonian star catalogues*. https://en.wikipedia.org/wiki/Babylonian\_star\_catalogues 4. NSW Education Standards Authority. (n.d.). *Year 11 Standard Mathematics: Working with Time* \[Sample Unit\]. [https://education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/mathematics/media/documents/ms-m2-working-with-time-sample-unit-s6.docx](https://education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/mathematics/media/documents/ms-m2-working-with-time-sample-unit-s6.docx?utm_source=chatgpt.com) 5. Wikipedia. (n.d.-c). *Babylonian astrology*. https://en.wikipedia.org/wiki/Babylonian\_astrology Previous Post ###### [Why Jack Reacher (probably) can't learn probability.](https://mathsthatclicks.net/blog/why-jack-reacher-probably-cant-learn-probability) Next Post ###### [Small Moments, Big Impact](https://mathsthatclicks.net/blog/small-moments-big-impact) ### Similar Blog Posts [![](https://mathsthatclicks.net/hubfs/genius-richard-feynman-and-modern-physics.avif)](https://mathsthatclicks.net/blog/a-bit-of-number-magic-engaging-students-and-showing-them-beauty) #### [A bit of number magic - engaging students and showing them beauty.](https://mathsthatclicks.net/blog/a-bit-of-number-magic-engaging-students-and-showing-them-beauty) [![](https://mathsthatclicks.net/hs-fs/hubfs/mandarin%20surface%20area_mehr.png?width=352&name=mandarin%20surface%20area_mehr.png)](https://mathsthatclicks.net/blog/discovering-the-surface-area-of-a-sphere-using-mandarins) #### [Discovering the surface area of a sphere - using mandarins.](https://mathsthatclicks.net/blog/discovering-the-surface-area-of-a-sphere-using-mandarins) #### [What does it mean to "understand" maths?](https://mathsthatclicks.net/blog/what-does-it-mean-to-understand-maths) [![Illustration5\_smaller\_sloganb](https://mathsthatclicks.net/hs-fs/hubfs/Illustration5_smaller_sloganb.png?width=200&height=206&name=Illustration5_smaller_sloganb.png "Illustration5_smaller_sloganb")](https://mathsthatclicks.net) ###### **© 2025 Maths That Clicks · All rights reserved** [Privacy Policy](https://mathsthatclicks.net/privacy) | [Terms of Use](https://mathsthatclicks.net/terms-of-use) | [Disclaimer](https://mathsthatclicks.net/disclaimer) [facebook icon](https://www.facebook.com/profile.php?id=61577172190302) [instagram icon](https://www.instagram.com/maths_that_clicks/) [youtube icon](https://www.youtube.com/@MathsThatClicks) [Follow us on Facebook](mailto:mark@mathsthatclicks.net) ```json { "@context" : "https://schema.org", "@type" : "BlogPosting", "author" : { "@type" : "Person", "name" : "Mark", "url" : "https://mathsthatclicks.net/blog/author/mark" }, "dateModified" : "2025-10-11T01:15:27.569Z", "datePublished" : "2025-10-11T01:15:27.000Z", "headline" : "The Maths of Time: Why Clocks Aren’t as Simple as They Look", "image" : [ "https://mathsthatclicks.net/hubfs/clock.png" ], "mainEntityOfPage" : { "@id" : "https://mathsthatclicks.net/blog/the-maths-of-time-why-clocks-arent-as-simple-as-they-look", "@type" : "WebPage" }, "publisher" : { "@type" : "Organization", "logo" : { "@type" : "ImageObject", "url" : "https://mathsthatclicks.net/hubfs/Illustration5_smaller.png" }, "name" : "Maths That Clicks" } } ```