Ancient Arithmetic: Newsletter Challenge (May 2018)

This is clickbait for math nerds. I don't have time for this. It isn't interesting enough to waste the time on it, but if it was, I would solve it in 3 minutes. I've already wasted too much of my all too short life on earth on it already.

Congratulations; you just wasted another minute on it.

More like a minute and a half. I type slow . . . . DOH!

Are we supposed to read the cuneiform version, versus the incorrect Arabic translation?

...is this Babylonian math equation correct?...

Yes...it's the interpretation that is incorrect...

Wait. So, the 'challenge' revolves around not being able to count these little triangles?

Ummm, that's kind of disappointing.

You are certainly welcome to delve deeper, I'm sure we can find a reasonably technical answer....I myself am no Babylonian math expert, in fact I'm no math expert at all....I do know that the order that functions are executed in, can be a tripping point for many....and have not heard of any higher math, other than addition, from the Babylonians....I think the Babylonians did have a zero though....

Rixter has the correct answer, with the necessary proof. The math here may not be generally know among non-math people, but it's simple for anyone who had high school math. I don't see what else there is to delve into.

If you say so....

SolarEagle has made very interesting comments. Allow me please to extend for those interested. Babylonians maths concept was based on base-10, same as us. Number names are 1 to 9 for digits, then in tens (semitic axra), hundreds (miya), thousands (elf), etc. So why use base 60?

Elsewhere, the 360 division of the year was dictated by a calendar technique. Season days can vary from 87 to 93, making 90 the best number choice divisible repeatedly (by 3, 3, 2, 5). System is explained here: https://melitamegalithic.wordpress.com/2017/04/17/melitamegalithic/

In agriculture, knowing the date when to sow grain was and still is, essential. That is before the winter solstice. The calendar is to find when that is. Engineering design par excellence.

What a load of baloney.

I put that comment to my earlier post to "educational shock". As said above by others, there is plenty of reason to delve into further (this being an education side to this site).

1. We use base 10, with ten numerals (including zero). We also use hex, base16 with sixteen numerals 0-F. The Mayans used a vigesimal system, base20 with 20 numerals. The Romans used a messy system, mixing bases to make it mathematically unwieldy. The Babylonians used base60, but expresses numbers in ten numerals on a base10 system. One should ask why. You will find good reason.

2. Why divide circle in 360? Leaves you with factor 5 which is an odd prime number in the end. The inch with binary division all the way to 64ths is convenient; more than metric (and i use both systems). Some say because the year was 360 days, which it never was because its shape is constantly changing, and the orbit is not circular giving different season lengths - this is not complex to understand.

3. The link in my earlier post predates the Babylonian system by some three millennia. The maths involved is simple, but equally, it leaves no other option for interpretation. Maths/geometry knows a much earlier beginning.

More baloney.

I think you mean babaloney....

Rixter is incorrect, SolarEagle is correct. The commas simply separate the positions of the powers of 60. ((60^2) x 2) + ((60^1) x 3) + ((60^0) x 17) = decimal (7,200) + (180) + (17) = 7,397.

I thought I broke all of my homework tablets so nobody could read my homework errors.

Is a comma (2,3,17) a mathematical operative?

Is this problem, as stated, correct?

I have found a reference....

"Here is the Babylonian example of 2,27 squared "...

http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_numerals.html

TY for that ref; very interesting to follow up. Ref says problem derives from tablet AO 17264 in the Louvre collection in Paris.

It is only part of a computation, but this is what is said of it: "Another such text is a single problem text containing a kind of “boundary value problem” for a trapezoid with sides of given lengths, divided into a chain of three bisected trapezoids (AO 17264; Neugebauer 1935, 126; Friberg 2007b, 292). The stated problem is to find out how the given trapezoid can be divided among six brothers so that the oldest brother and the next one get trapezoidal shares of the same area, so that numbers 3 and 4 get the same, and also numbers 5 and 6. See Fig. 6.1 below. The student who wrote down his solution to the problem cheated blatantly, but managed to find the correct result (which he obviously knew beforehand) through a couple of nonsense calculations." Link: https://core.ac.uk/download/pdf/70605689.pdf

Which makes SolarEagle's link interesting for the questions it raises. We have inherited from the Babylonians the division of the circle, and the division of time. But nothing is known of its origin, or why it was adopted in the first place. Except what I started with in my first post; a need for dividing a quadrant by 90. Easiest start is to divide quadrant by its radius, in thirds, thus giving circle division by 12 (time). Quadrant division by 90 giving circle div by 360; (then circle circumference divided by radius gives 6 parts of 60). What is important here is that now the evidence is there (like it or not).

Yes exactly, there are several translations that could apply here, without knowing the context in which this calculation was used, it's just a guess. It's like back of the envelope calculations, the guy that writes it has a better understanding of what he's looking at then some random passerby. Is it correct, yeah could be (haha).

The commas separate the powers-of-60 place holders, and are necessary in this case because our decimal numbering system is composed of only 10 single digits, not 60 single symbols as would be necessary to write base 60 numbers without commas. For example, if this was simply written as 2317, it would be calculated as (2*60^3) + (3*60^2) + (1*60^1) + (7*60^0), yielding 225,867. With the commas it comes out as (2*60^2) + (3*60^1) + (17*60^0), yeilding 7,397. WahLah!

Answer is posted in the original thread.