Why did ancient Egyptians forbid using the same fraction twice?

>>8814612
I'll just hop into my Tardis and go ask them. brb

>>8814612
>forbid using the same fraction twice
???
That's not how it works.

They just don't allow anything but a 1 in the topside.
They just hadn't thought of the idea that they could do that.

>>8814621
I'm back. Apparently, they don't speak english. Gonna learn some ancient egyptian, brb

>>8814612
I guess they didn't think of fractions the way we do. To understand why exactly, I guess the best way is to dwelve into their calculus algorithms, to understand their point of view. This is a difficult topic.
I had a math history class with a teacher in that kind of stuff, who wanted to make it very clear that egyptian, babylonian etc way of doing math was not "retarded", but rather evolved and consistent, and sometimes more powerfull than our system of representation.

>>8814612
They did. 2/3 = 1/3+1/3.

They only allow 1 in the numerator so if the denominator is even 1/n+1/n is more efficiently represented as 1/(n/2).

>>8814641
If I remember well, they did that only for a few numbers as the denominator.

Here's a babylonian algorithm for solving linear equations. It's rather simple compared to other stuff. Of course the base 60 and their method of notation and calculations make it hard to understand.

> [My barleycorn] was stored in the market gate, then (someone) took a 10th of it, and I took a 3rd of it, then I remeasured the remainder of my barleycorn:
> precisely 1 (bariga). What was the initial amount of my asset?
> When you work it out, since “a 10th and a 3rd” were stated,
> you shall note down 10 and 3.
> You shall solve (calculate) the reciprocal of 10, then you shall raise (multiply) it by 1, your barleycorn:
> you will see 6.
> You shall tear out (subtract) 6 from 1: you will see 54.
> You shall solve (calculate) the reciprocal of 3, your 3rd: you will see 20.
> You shall raise (multiply) 20 by 54: you will see 18.
> You shall break off (subtract) 18 from 54: you will see 36.
> You shall solve (calculate) the reciprocal of 36, then you shall carry (multiply) it by 1,
> the remainder of your barleycorn
> you will see 1 (bariga) 4 (bán), the initial amount of your barleycorn.

File: smf_rhm_11_7-21.png (70KB, 826x1169px) Image search: [Google]

70KB, 826x1169px

This is a quadratic equation solving algorithm.


The area and side of my square I added: 0 ; 45
You, put down 1, the projection.
Break 1 in half.
Multiply 0 ; 30 and 0 ; 30
Join 0 ; 15 to 0 ; 45 : 1.
1 is the square root (of 1).
Subtract the 0 ; 30 which you multiplied in the 1: 0 ; 30
The side (is) 0 ; 30


Some guy gave a very nice geometric interpretation, which makes it seem like all they were doing was put the equation in canonical form, with geometric constructions.

>>8814612

Well, it would be a bit redundant, wouldn't it? Some of this is down to taste.

For the ancient Egyptian, the ideal representation of a fractional quantity was its expression as a finite series of distinct unit fractions. The example par excellence is problem number 31 of the Rhind papyrus, where the solution of a linear equation in one variable is correctly expressed as an integer part, together with a long, autistic chain of seven unit fractions:

https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus#Content

(scroll down a bit). Further, as the OP picture hints, the ancient Egyptian was pre-occupied with /Horus Eye Fractions/, which are precisely the unit fractions with denominator being a power of 2, from 2-64. See problems 47, 64 and 80 in the above link for fairly organized (yet still not totally consistent) examples of repeated use of Horus Eye fractions in calculation tables.

Obviously, the insistence on distinct denominators is exactly at odds with what actually simplifies the process of adding fractions, /finding common denominators/. This is why, according to mathworld, Andre Weil characterized the Egyptian fraction as "a wrong turn": http://mathworld.wolfram.com/EgyptianFraction.html

Still, the Egyptians (their elite scribes, anyway) could /correctly reckon such onerous strings of information/, that is, correctly add fractions, which is more than can be said for over half of the modern population at any given moment. The Egyptian's actual mathematical failings, so far as Rhind allows us to see them, were certain confusions about geometry and dimensional analysis (but even so, he had a decent bit of primordial number theory and linear algebra per same document). They don't /really/ have elementary algebra just yet, either, based on this one data point, just the beginnings of it.

Erdos et al have proposed a still-open problem, relating to series of unit fractions:

https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Straus_conjecture

>>8814904
This reminds me of what the teache was saying, about why these ancients mathematics could seem a bit retarded but were not so much :

These people were preocupied with other metaphysical problems than we are, and their mathematics and the way they developped were in par with these metaphysical problems.
For example, the greeks tried very hard to quadrate a circle.