So have you ever wondered why there are 360 degrees in a circle? Or why there are 60 minutes in an hour? or 60 seconds in a minute? Seems rather weird doesn’t it. Well, don’t worry – it’s not an evil conspiracy.

**Simple Answer:** Blame the Babylonians – they used the Sexagesimal system. Don’t get excited – it means that instead of using base 10 (as we do) they used base 60. You can read more about it on wikipedia.

**Geek Answer: **So the next question is, why 60? Well, 60 has a lot of advantages, especially before the day of calculators. The numbers 1-6 all divide nicely into it – therefore it’s easy to split a circle / hour / minute into fractions and get a whole number back (e.g. 1/4 hour is 15 minutes, and 1/6th of a circle is 60 degrees). Not only that, 10, 12, 15, 20 and 30 all go into it as well! All up, that means you get 12 factors (or easy fractions). That’s awesome. Just don’t ask them to divide by 7… (1/7 = 0.08:34:17:08:34:17: reoccuring)

Compare this to base 10, where you only get 4 (1,2,5,10) – even with 100 you only get 9 (1,2,4,5,10,20,25,50,100).

**But why 60**? Dustmop (below in comments) points out that farmers probably counted the days in the year long before they cared about algebra. Combined with the fact that 360 is very close to the 365 days in a year, probably lead to the number being used in a lot of primitive seasonal calculations. The Babylonians probably got the idea of using Base 60 from this even earlier origin. If there are ETs out there, I wonder what base they use for chopping up time (considering it’s unlikely that they have the same 365ish rotations per cycle around the sun) and circles (probably radians)?

**Update 2009: **There is a much more comprehensive explanation here: http://scienceray.com/mathematics/applied-mathematics/why-are-there-60-minutes-in-an-hour/

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Huh? 18 goes into 60?

Well yeah in the same way that 7 goes into 15.

If you’re talking integers, I’m not sure I follow?

Maybe replace “18 & 20” with “20 & 30”?

Hehe – yeah, I was telling someone about my entry as I was walking to Shake Shack and realized that I had put 18 in it :) Fixed now – thanks.

I think you may have confused 60 with 360 there — neither 8 nor 18 evenly divide 60.

PS, by your number of divisors logic, I guess we should have wished for 420 degrees in a circle:

{1,2,3,4,5,6,7,10,12,14,15,18,20,21,28,30,35,36,42,…}

Yeah – that’s the mistake I realized I made as I was walking :)

As for 420, I guess the brits did do 400 (gradians) :)

i too got a different idea, can we replace hours and minuts format with only 0 to 360 numbers ??

i mean 00:00 = 0,

1:00 am = 15,

2:00 am = 30,….

24:00 or 12 night = 360 ??????

if you ask time you will answer with a single number ‘180’ !!!!

so single number can represent the time…..

may be for programming this is easy ?

Early farmers after the agricultural revolution had a lot more incentive to follow the sun than easy algebra. This is why they picked 360 for degrees in a cirlce, it was close enough to how many days were in a year (the original circle). The Babylonians just stuck with it.

60 is probably the common multiple most convenient for merging two common number bases: duodecimal (12) and pentadactylic (5 or 10). We still use (independently evolved) duodecimal systems (12 inches per foot) and still have 5 fingers per hand. The sexagesimal system probably arose after one of the many conquests of Mesopotamia by outsiders (long before Babylon!). The new accountants totted up the lucre in their system based on records ept in the erstwhile system.

Thanks!

From a practical standpoint, it all begins with the circle being used as a tool for making observations whether heavenly or for more earthly subjects. To use it as a tool for direction, elevation, etc., if you divide a circle in half, then quarters, then eighths and so on, the smallest practical unit for a high degree (no pun intended) of accuracy within that circle initially could easily be judged to be 1/360th, hence 360 degrees for a full circle would be indicated.

It’s not so much that it’s easy to split a circle into 360 as it is that the circle dictates that division by it’s very geometry. The same can be said of 60 for a less demanding role, the circle dictates it.

But if you keep halfing it like that, you get 256 and 512 (base 2) rather than 360?

So has anyone figured out why there are 10 hot dogs in a pack and only 8 buns?

Xbox 360! lol

If they bring out Civ 4 for the Xbox 360, I am so playing the Babylonians! :)

[…] 360 in a circle, 60 minutes and 60 seconds… What is so special about 60? So have you ever wondered why there are 360 degrees in a circle? Or why there are 60 minutes in an hour? or 60 seconds in a minute? Seems rather weird doesn’t it. Well, don’t worry – it’s not an evil conspiracy. [link] […]

The two extra hotdogs are the ones that get dropped into the campfire ;)

That’s why there’s a “six-pack” of beer…to go with each surviving hotdog.

Alot of older calendars only had 360 days on them. The extra 5 days were considered days for the gods and not counted.

I think it would all stem not from farming but from the need to finally be able to plan travel in the need to find food. we were not farmers originally we migrated like all animals until we realized we could create food out of the earth. So it would be essential to be able to plan ahead somewhat to move when the seasons were to change. Of course this would have been at first done by following other animals already sensing the coming changes. finally some one would have started to mark the number of sunrises between winters originally (being the major change of all the seasons ) and would have probably had a number of close to the 365 and rounded it off to 360 this of course would have slowly been refined by the following of the seasons which at first would probabl;y only have been the good season and the bad season (summer and winter) then realizing that the worst of the bad lasted a certain amount of time(again tracked by simple scratching marks in a tree) and the best of the good season and realized that they were in a somewhat 90 day endurance..ofcourse the 90 would have been rounded off to by wahtever the number really was thast was monitored.. And used because it fit into the 360.. Now we would have had 2 periods defined with two left over and the would have just been known as pre real good and pre real bad. (spring and fall..Now we have a 4 period year…

I would assume this would have been used instead of months for a long long time.. until the actuall major settling of humans becoming year round stationary beings instead of migratory..

I believe all of the major work done in creating the day hour etc would have been done by astronomers (of course they would have been more scientists than just astronomers as mathmatics would have played a role and trial and error etc..) but the fact that the stars are far more desriptive of the passage of time thatn the sun is ( meaning the passage of time can be seen far more clearly watching the m ovement of stars than watching the sun although both move the stars are far more descriptive…

Wow I have to stop now I real do ramble on about nothing..

Uhh this has no basis in fact and is only the Ramblings of a Madman (my blog) if you want more..

I like to try and define things based on my own experiences and views sometimes i am right other times i am right…If you want to know if you are right just comnpare your answers to mine and if they are the same You are right

Bye

As for the question about 10 hot dogs and only 8 buns – it’s for your friend that’s on the atkins diet :)

Here’s my theory.

Recreate a sundial.

Divide the day into equal parts

using simple tools.

With a compass it is EASY to divide a circle into 6 equal segments. It is then easy to do 12 etc.

The basis of 6 was for convenience of construction.

[…] Ever wonder why are there 360 degrees in a circle and 60 minutes and seconds? […]

I thought that the duodecimal system came from the fact that you can count up to twelve on the phalanges of one single hand, pointing them with the thumb of the same hand…

Twelve phalanges times the five fingers of the other hand = 60.

It’s easy to divide the circle in six equal parts using a pair of compass…

6 * 60 = 360…

great post. love the format of the entry. “Question. Simple Answer. Geek Answer. ETC.” I’ll have to borrow it someday.

60 seems to round nice earth orbit wise, while atomic clocks might says its off by a second or so its good enough and serves as a common reference.

One of the earliest uses of numbers was counting livestock. You can count up to 60 easily with both hands.

Using the thumb of one hand as a pointer, count the segments of the remaining four fingers on that hand. Three segments per finger equals 12.

You mark this off by holding down one finger on your other hand. Then start again. You have five fingers on your hand: 5×12=60. Then you make a mark on the wall or whatever.

This way, you can count large numbers of animals using only your hands. This is also the reason why our numbers go eleven, twelve; rather than oneteen, twoteen.

At least that’s what Johnny Ball used to say.

Take a day off guys. Uh!! that’s it!!! farmers take a day out…so it really is six days. Solved.

PS It’s still the 20th Where I am.

Oh my gosh! This is the highschool nightmare all over again. I’m outta here! lol.

I find it amazing how this post created a whole wave of responses. Trigger! Many different answers, all intelligent & interesting, however nobody has the answer – and why should one? However personally I also believe it has to do with the seasons & the sun. Which is round.

Feeding off of Livetoad above (comment 6). Back when I was a teacher, I had textbooks to that could back this up, but here’s a more involved explanation.

In the ancient near east, there were cultures that had a base-5 or base-10-based system. The base-5/10 system is a natural counter, what with five/ten fingers and all. We still use base-5 when counting using hash marks (note the hash marks’ similarity to cuneiform).

It is also well-documented that there were base-12 cultures in that area. Why base-12? Basically, using the explanations of Pygy and phillbarron (comments 20 and 23) make – using the thumb as a counter of finger segments. People still count that way (my non-ancient non-Sumerian non-farmer father, for example).

Cultures using the two counting systems likely “merged” during the rise of Babylon – the only way to merge the counting systems was getting to base-60 or base-120.

This fit nicely with the natural world they observed – 30-day lunar cycle, 360-day year. The circle was based on their estimation of a year. Then their early mathematicians divided circles into degrees to represent days, and 24 hours. The 24 hours likely comes from the 12 sunup and 12 sundown hours of the equinoxes. Later mathematicians divided hours into minutes and seconds. From there, we get our temporal uses of minutes and seconds.

Whew!

Oops… I should have written: “Then their early mathematicians divided circles into degrees to represent days, and 24 hours

per day/degree.”Also forgot to note that science still uses hours, minutes, and seconds as divisions of degrees (like GPS).

Wow I can’t understand…

Pakcar

Thanks for such an informative post.

[…] 360 in a circle, 60 minutes and 60 seconds… What is so special about 60? « Erudition Ambush Les Babyloniens et le Système Sexagésimal (tags: cool) […]

Very interesting…I think that there is usually a historical, theological as well as a mathematical link to the use of numbers, especially the one’s that we use daily. Numerology etc..The Babylonians and phoenicians, Sumarians, would not have separated the “science” with the “theology” and they have significance which is usually misunderstood, overlooked or just misinterpreted to this day…so you are right.

I like 12 hours in a day, 12 months of the year, 12 signs of the Zodiac, 12 diciples…12 everything

12 “hours” in the day after the Egyptian “HORUS”, which traveled across the sky (through the 12 houses). the 12 that have alway’s represented the 12 signs of the Zodiac. The Sun (lucious..latin for light) traveling across the sky for 12 hours, through the 12 houses….which is why the light and the good (the sun) is symbolised by LUKE SKYWALKER (light, across the shy, representing the sun)…for a fun example. then SET (the evil Egyptian god) comes up…just as it does today…with the SUNSET

anyway…i’ve never been any good at maths!

Cool blog!

ET’s would probably eventually wind up with a numeric system based on the number of digits they have or the number of tentacles or whatever, regardless of their planet’s solar cycles. Of course, if they’re telekinetic, then this theory’s pretty much screwed. Heheh. ^__^

lovely article. I just loved the whole hypothesis

numbers are surprisingly rad.

This is interesting. I’d never questioned 360 degrees or 60 minutes, but history is always rewriting itself.

For some more theory, albeit a tad more on the satire side, check out my new blog:

http://underdogs.wordpress.com

While the Babylonians had a large base for their number system, whoever created the British “Imperial” units used a *binary* system.

very interesting

This naturally leads on to why the days are in the order they are and not the order of planet orbit length.

12 divides up the year because of the lunar cycle.

7 divides up the month because of there being approximately 28 days in a lunar month.

There were 7 planets (the ‘wanderers’ which in Greek is planetes) so mankind thought there was a fundamental link.

By the time of the Romans they were known as the Moon, the Sun, Jupiter, Saturn, Venus, Mars and Mercury.

Saturn – 29 years

Jupiter – 12 years

Mars – 687 days

Sun – 365 days

Venus – 225 days

Mercury – 88 days

Moon – 28 days

So why does the order of the week not follow the order of ‘dominance’ of the planets?

It is all down to the fact that the planets were originally used to name the 24 hours of the day not the days of the week.

Consequently the first hour would be Saturn and hour 24 would be Mars, the first hour of the following day would therefore be the Sun hour, the next day’s first hour would be called the Moon hour and so on. Gradually the first hour of the day became known as the ‘dominant’ planet and the day named after this dominant planet. So it was all down to the fact that 24 divided by 7 leaves 3 remainder and the cycle repeats on the eighth day.

If all 10 planets had been visible to the naked eye would we have had a 10 day week, 30 day month. More work, fewer week-ends?

Your post wasn’t entirely clear in some places. Different cultures used different week-cycles; the Romans used eight-day weeks, the Egyptians and Chinese used ten-day weeks.

So, nobody likes the hour/day thing then?

[…] Why 360 degrees? Why 60 minutes, or 60 seconds? Answer: Babylonians used the sexagesimal system (base 60). (tags: useful reference) […]

Iam a year 6 student trying to do a science/time project containing questions such as “Why do we have normal years and leap years”. My irrational/stupid/lazy partner and i have been having great difficulty in fiding answers can u plz help us?????? thankyou

Actually the concept of 360 degrees dates far before the Babylonians in some science/sacred text in India called the Vedas. Do a google search on “360 and vedas” and also have a look at this link

http://en.wikipedia.org/wiki/Circle

and

http://www.vedanet.com/index.php?option=com_content&task=view&id=65&Itemid=2

Having just taught students that for every 15 degrees of longitude there is 1 hour, how can I now tell them that 1 degree is equal to 60 minutes…60 seconds in a minute …without confusing the heck out of them.

Actually, I Googled “360 and vedas”, and all I came up with was this page!!! You’re silly, Sanjay

I would also like to point out that all circles naturally subdivide into 6 parts. The way you discover this is by getting out 7 pennies or quarters or nickels (all 7 must be the same size). Put one coin in the center, and put the others around it, each touching the coin in the center and touching its neighbor on each side. You will find that 6 coins perfectly fit around the center coin. This is nature’s built-in geometry. Now draw a line from the center of each outside coin to the center of the inner coin, and you fill find your inner coin equally subdivided into 6 parts. This geometry finds expression in many repeating hexagonal patterns in nature that are in essence neighboring circles with edges flattened where they touch: (for example, honeycombs, flower seed pods, flower petal arrangements) You could alternately think of hexagons as touching circles that have expanded to fill in the gaps between the circles.

Once you have subdivided your ‘perfect number’ 7th middle coin into 6 equal subdivisions by the 6 coins that surround it, subdividing each of those 6 regions by 10 may not be a stretch for a society whose individuals have 10 fingers.

In summary, 6 natural subdivisions, each divided into 10 fingers or toes, gives you 60 subdivisions to a circle.

The week is the only unit of time that has no explainable origin other than God himself. You can argue that there are 7 wanderer planets till you’re blue in the face, but it would make ZERO SENSE for ancient cultures to impose a repeating pattern of 7 days on top of the natural rhythms they observed (year/month), because the 7-day week doesn’t even remotely fit those natural patterns. Those who think that months are ‘about’ 28 days and therefore even multiples of 7 days should live in Israel or an Islamic country for 10 years and then come back and tell me which day of the week the lunar-based (month-based) feasts fall on. The answer is…’it varies, because the lunar monthly cycle and the weekly 7-day cycle are completely out of sync.’ The lunar month is not ‘about 28 days’. The lunar cycle is 29.53 days, about 1 1/2 days longer than 28 days. After just two months, that means you’re over half a week off! Therefore, certainly nobody who has ever lived according to lunar calendars would try to propose such an obviously make-believe correlation between weeks and months. Only armchair theorists who live in the modern Gregorian calendar with its manufactured ‘months’ would try to draw a correlation between the lunar month and the 7-day week. The origin of the 7-day week can only be attributed to ‘religion’ – to God’s instruction to mankind to rest every 7th day. The 7-day week is not of human origin, because there is no observable natural pattern to base it on. Even the ancients knew the difference between the moon and the planets. That’s why they based the MONTH on the MOON. To then turn around and include the MOON as a WANDERING PLANET would be double-counting the moon but single-counting the planets. The ancients were smarter than a lot of folks give them credit for being. Not every ancient man lived in a cave and scratched his flea-infested armpit with hairy, dung-covered fingers – it just so happens that all the other homes the ancients lived in besides caves didn’t last as long as the caves, so if the oldest human habitations we discover in the 19th & 20th centuries are caves, then all I can say is…duh! Do you expect an 8,000-yr-old straw house or fabric tent to still be standing in Mesopotamia? (Or a wood boat on Mt. Ararat?) Back on the subject, as we attempt to find some natural occurrence to base a week on, we might as well choose a 5-day week or an 11-day week. The 7-day week just doesn’t make sense from any naturally observable phenomena.

Not altogether true Waka-man. There IS a astronomical phenomenon to base 7 day weeks on! However, this can only be understood and seen in conjunction with religion. In Exodus chapter 20 the instruction is to work six says and rest on the 7th day. This isn’t an instruction particular to an order of days, but rather a principle of how many days in a row one can work without stopping. Scripture instructs we are only allowed to work six days in a row, then cease from work.

In addition, there is also an instruction in Exodus, Leviticus, Ezekiel, Psalms and Numbers regarding the New Moon Day (Dark Moon) as the beginning of a month AND a “worship” day, different from a 7th day rest or Sabbath. Thus, Exekiel 46:1 explains that there are three (3) different types of days. 1. Sabbath days 2. New Moon days 3. Working days.

Here is how this all works together: On the New Moon day, Torah keepers did not work because it was a “worship” day. This is the FIRST day of the lunar month. The second (2nd) day of the month carries no instruction so it is assumed that work can be done on that day. The same with the 3rd, 4th , 5th, 6th and 7th days of the month. However, when you reach the eighth day (8th) day, you must rest because the fourth commandment requires work no more than 6 days in a row. The 2nd thru the 7th, six days, then the 8th day is the “seventh” day AFTER six days of work and one must rest. Therefore, the “seventh day” Sabbaths, by default, ALWAYS occur on the 8th, 15th, 22nd, and 29th days of the LUNAR month.

By simply following the principle of worship days, work days and sabbaths, the sabbaths AUTOMATICALLY fall on the 8, 15,22, 29th days. You may call it coincidence or divine ordinance BUT it just so happens that the moon PHASES change almost perfectly on these days. half-moon (8th), full-moon (15th), half-moon (22nd), wanning crecent (29th). So if one was to “lose track” of the sabbath count, one could find it again in the luminaries of the sky, namely, the moon.

So this is where all the freakish nerds hang out ? Cooool !

The seven day week makes perfect sense when you realise that the English word “seven” derives from the Babylonian word “bollox”- a word I’m guessing was just on the tip of your tongue !

what the hell are you talking about

[…] fore info check out Shaun McCarthy’s blog or see what Dr Math has to say about it! You can also read more about Sexagesimal on […]

…well you guys are all kinda odd…and btw this passage hardly helps anyone looking for information…

why make the 360 degree circle seem so hard?

the old-timers were geometers; you know, compass

and straight-edge constructions!! take a regular

triangle X a regular square X a regular pentagon

X a regular hexagon … 3 X 4 X 5 X 6 =???

Now, is that so tough ?? The old boys may

even have played around with gears. Note that

2 sides doesn’t make a polygon;and constructing

a seven sided regular polygon is not possible.

So, give it a try, it’s easy!!

hbbbbbbbbbbbbbbbbbbbbbbbbbbhhhhhhhhhh

Correction to waka-man’s post:

A lunar orbit (wrt stars) is about 27.3 days and a lunar day(wrt sun) is 29.5 days as it is also going around the sun. So an average of 28 days is not that far off.

Ancient cultures used moons to help calculate time. The moon orbits the earth less than 13 times in a year and 12 goes inot 360 evenly is why they rounded off.

Easier to explain to an illiterate sheep hearder or fisherman in ancient times…cuts down on bar fights.

Wm Will, why do you say “a seven sided regular polygon is not possible”?

Good to read.

Hello. And Bye.

Cool! This was my homework, so ty :p. Interesting too!

Ty again, and BTW, is this y we used imperial Ft and inches? coz it made me wonder. And if this is already posted, soz, but CBA all the comments. Tyvm!

dude you know what I’m talking about! soy desole

i tried counting with my thumb as a marker for every 5 fingers i count on my other hand

but i got 16 marks not 12 (the top of the fingure)

5*12=60

5*16=80

so nice try but not practical answer for why 60

if they need to count they would have counted as much as they can and that would be base 80

No. If they needed to count as much as they could just using their fingers they would’ve used base 6,400. 80 phalanges * 80 phalanges (rather than 60 phalanges * 5 fingers). Is that really practical?

Wow, 60 comments from Sept 2006 to Feb 2009 – I couldn’t walk away. What a great read!

The people who built Stonehenge – in its early phase could do a very accurate 56 gon which means they could do a very accurate heptagon – all from square and circle geometry, in fact it’s very easy to draw and the simplest approximation to a heptagon known (only recently discovered, and published as ‘Johnson’s method’ of creating a heptagon).

see:’Solving Stonehenge’ by Anthony Johnson

Great job with the info. How did you find it? Please let me know.

Thank u very much for that successfull performance.Nice blog.

Glad you!Whats the weather like today ? Thank u ! sa? ekimi

Thanks good great article

Sağlik haberleri

It is given in Rigveda. It was easy for a student studying the nature, that celestial position is repeated almost after 12 full moon nights of 30 days. They possibly assumed that skies are moving from east to west in a circle around the earth. They were not aware that earth is rotating around Sun. They thought that Sun, Moon and stars are going in circle around Earth and one such circle is completed in 360 days. Change in position of one day was accounted as one degree. Later mathematicians must have refined it smaller parts of minutes and seconds for further detail studies of astromony.

good site!

I assume that the base 256 in the angular division of the circle is probably more common in the univers the the 360 division, who had more relation to orbital time, than to geometrie… altought it does do th job?!

hi

I think,I believe all of the major work done in creating the day hour etc would have been done by astronomers (of course they would have been more scientists than just astronomers as mathmatics would have played a role and trial and error etc..)by fue

I find it amazing how this post created a whole wave of responses. Trigger! Many different answers, all intelligent & interesting saç ekimi

really I have never wondered…interesting

neither did i except our teacher got us to find out for homework

Hello

u can tell i like ponies

and pigs and dogs and owls

and spiders

Hello u people

I just work in the transfers arena, but its amazing how such a random post can actually make people think so much.

Very interesting stuff. Many thanks for that article!

Thanks for helping me with my maths homework!!:)

never thought about this

God created his stuff in 6 days and rested on the 7th

hmmm funny

Your blog is pretty cool to me and your topics are very relevant. I was browsing around and came across something you might find interesting. I was guilty of 3 of them with my sites. “99% of website managers are guilty of these five mistakes”. http://tinyurl.com/bn4kol9 You will be suprised how fast they are to fix.

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