So, rather than write about it, I will write about another one of those marvellous things that have no point at all but which I find massively interesting. This time it is about why are there 360 degrees in a circle. I can do maths, so find stuff like this inordinately fascinating.
In school we learn there are 360 degrees in a circle, but where did the 360 come from? When it is pointed out that the Babylonians counted to base-60, rather than base-10 as we do, people often ask if there is a connection. The short answer is no. The longer answer involves Babylonian astronomy.
So it was mostly the Babylonians ... But then also the Greeks.
So it was mostly the Babylonians ... But then also the Greeks.
It also involves calendars and most importantly a phenomenal amount of data gathering. Interesting parallel with you know what today as the experts from today go on all the time about the need for lots more hard data before they can know how to deal with things.
The Babylonians began observing the stars and various constellations around 2000 BC (according to the earliest texts), in the southern city of Uruk referring to a festival for the goddess Inanna so it was probably earlier than that. It all started with Venus being the brightest 'star' (no telescopes so look at the nearest/brightest object in the sky) and pretty soon they figured out that Venus along with the moon and other planets they could see lie on the same great circle, called the ecliptic, which had as its reference point the Sun as seen from Earth during the course of a year.
In order to record all this accurately, they needed a calendar as well as a method of recording positions along the ecliptic.
So calendars. The clever Babylonians figured out that it was the different phases of the moon which formed a rhythm in the life of their (and in fact all ancient) cultures, so that's where they started. Day 1 would be the evening of the first crescent at sundown.
With good visibility, a lunar month lasts 29 or 30 days and by about 500 BC, the Babylonians had discovered a scheme for determining the start of each month.
This used a 19- year cycle: 19 years is almost exactly 235 lunar months and the scheme works on seven long years (of 13 months) and 12 short years (of 12 months). This led to a fixed method of interleaving long and short years, still used today in the Jewish calendar and everything in the Christian year based on the date of Easter.
This phenomenally almost impossible to believe calculation (certainly when you think that our calendar these days is fixed and probably like me, most people wonder why the days of Easter, or Chinese New Year or some other dates change every year, well now you know) were derived by these amazingly clever Babylonians who started to record their observations.
This phenomenally almost impossible to believe calculation (certainly when you think that our calendar these days is fixed and probably like me, most people wonder why the days of Easter, or Chinese New Year or some other dates change every year, well now you know) were derived by these amazingly clever Babylonians who started to record their observations.
The records that helped them discover this cycle began in the mid-eighth century bc, when Babylonian astronomers wrote nightly observations in what we now call ‘astronomical diaries’. These continue until the end of cuneiform scholarship in the first century ad, yielding eight hundred years of astronomical records: a terrific achievement, far longer than anything in Europe to this day. It facilitated great advances, notably their discovery of the so-called Saros cycles for predicting eclipses. Each one is a cycle of 223 lunar months, perpetuated over a period of more than 1,000 years. There are Saros cycles operating today first seen in the eighth and ninth centuries. They remain the basis for eclipse prediction and appear in detail on the NASA website.
800 years in those days was maybe 30+ generations given an average life span, enough for even the pickiest expert who wants data to prove a theory. Also a phenomenal achievement of relentlessly recording what to many must have seemed to be arcane nonsense but which today has a basis in almost everything that we do.
Once they had the calendar and could see that an annual cycle of life encompassed broadly 12 months, they were on the way but had to move onto problem two: method of recording positions along the ecliptic.
As it happened, the Babylonians seemed to like the organisation of 12 so split the months into smaller units of measurement. Obviously one day is one day but what about the time during the day? Again obviously you have before midday and after midday, so they decided to split both these periods into further units of 12. They also liked 30 as 30 was the usual number of days in a month so they further split up these units of 12 by a further 30 so as to be able to record data in their astronomical diaries more accurately, using fractions.
As for the sky, the firmament, the stars along the eliptical, well that was easy too now. They split the elliptical up into 12 sections:
As Greek geometry developed, it created the concept of an angle as a magnitude – for example, adding the angles of a triangle yields the same as two right- angles – but in Euclid’s Elements (c.300 BC) there is no unit of measurement apart from the right-angle. Then, in the second century BC, the Greek astronomer Hipparchos of Rhodes began applying geometry to Babylonian astronomy. He needed a method of measuring angles and naturally followed the Babylonian division of the ecliptic into 360 degrees, dividing the circle the same way. So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy.
So there you have it. Why 360? Fascinating. Here's the full article.
800 years in those days was maybe 30+ generations given an average life span, enough for even the pickiest expert who wants data to prove a theory. Also a phenomenal achievement of relentlessly recording what to many must have seemed to be arcane nonsense but which today has a basis in almost everything that we do.
Once they had the calendar and could see that an annual cycle of life encompassed broadly 12 months, they were on the way but had to move onto problem two: method of recording positions along the ecliptic.
As it happened, the Babylonians seemed to like the organisation of 12 so split the months into smaller units of measurement. Obviously one day is one day but what about the time during the day? Again obviously you have before midday and after midday, so they decided to split both these periods into further units of 12. They also liked 30 as 30 was the usual number of days in a month so they further split up these units of 12 by a further 30 so as to be able to record data in their astronomical diaries more accurately, using fractions.
As for the sky, the firmament, the stars along the eliptical, well that was easy too now. They split the elliptical up into 12 sections:
the ecliptic was divided into 12 equal sections, each split into 30 finer divisions (also called uš), yielding 360 uš in total. For finer accuracy an uš was broken down into 60 divisions. Each of the 12 sections they labelled by a constellation of stars and, when the Greeks took on Babylonian results, they preserved these constellations, but gave them Greek names – Gemini, Cancer and Leo – most of which had the same meanings as in Babylonia.
Sadly for them at least, by this time the Babylonians passed into memory and were overtaken by the Greeks who thankfully had similar interests and courtesy of no TV or internet, plenty of time on their hands too. So they developed Geometry single handedly bringing order to many things at the same time as creating a method by which children of the future could legally be tortured (actually I liked geometry and particularly the acronyms by which we remembered various geometrical terms and calculations).
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| My sign Pisces |
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| The quadrants of a circle. How we remembered which quadrant at school was ASTC which stands for All, Sine, Tangent, Cosine or in schoolboy parlance All Sausages Turn Cold. Moving one step further into the calculations of the various functions: Sine is opposite/hypotenuse, Cosine is adjacent/hypotenuse, Tangent is opposite/adjacent. This was wonderfully learned as Some Old Hags Can Always Have Their Oats Anytime. I did enjoy Geometry. |
As Greek geometry developed, it created the concept of an angle as a magnitude – for example, adding the angles of a triangle yields the same as two right- angles – but in Euclid’s Elements (c.300 BC) there is no unit of measurement apart from the right-angle. Then, in the second century BC, the Greek astronomer Hipparchos of Rhodes began applying geometry to Babylonian astronomy. He needed a method of measuring angles and naturally followed the Babylonian division of the ecliptic into 360 degrees, dividing the circle the same way. So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy.
So there you have it. Why 360? Fascinating. Here's the full article.
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