## September 19, 2007

### By the rivers of…

What is this? And what is its claim to fame?

this may help a bit more

Unearthed by: **Abhishek , ramsaravana , nihit , Gammafunction , Vinod , uma , Sharath , Swetha , Arjun June , Tathagata Chatterjee , shivani , yaksha , srichand.**

This is the famous root(2) tablet, pretty much the first known reference to an irrational number. See Abhishek or Yaksha’s comment for more details :)

First example of cuniform writing from mesopotemia. perhaps first example of symbolic writing ?

The first lunar table? (found in Babylon)

The famous ‘root(2)’ tablet from the Yale Babylonian Collection. . This tablet

consists of a drawing of a square with its diagonals also included. Next to one side of

the square is the Babylonian representation of our number 30. Near the intersection of

the diagonals are the numbers we would represent as 1.41421297 and below that

42.4263891. No explanation is given. However, based on the geometry and how close

the number 1.41421297 is to 2 (1.41421356 to the same number of places), it is clear

that the tablet shows how to calculate the diagonal of the square by giving a value for

2 and 30 2 , which would be the length of a diagonal of a 30 by 30 square.

In

addition to showing that the Babylonians knew of the Pythagorean theorem, over 1000

years before Pythagoras lived, it also shows an extremely accurate approximation of

2 .

Square root of 2… sq root of 2 is 1 + 24/60 + 51/60^2 and so on…………..

Square root of 2…..

Babylonian clay tablet YBC 7289…

The Babylonian clay tablet YBC 7289 (c. 1800–1600 BCE) gives an approximation of suqare root of 2 in four sexagesimal figures, which is about six decimal figures.

I do not understand too much more…

Babylonian clay tablet giving an approximation of root 2 in sexagesimal format.

Babylonian clay tablet YBC 7289 with annotations. The diagonal displays an approximation of the square root of 2 in four sexagesimal figures, which is about six decimal figures.

The Babylonian system of mathematics was sexagesimal (base-60) numeral system. From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60×6) degrees in a circle.

Our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, the Pythagorean theorem, and the calculation of Pythagorean triples and possibly trigonometric functions.

by the rivers of babylon…..the mention of asger aaboe gave it away

both the pics are the famous ‘root(2)’ tablet from the Yale Babylonian Collection.

This Babylonian cuneiform tablet YBC7289, gives the square root of 2 as 1, 24, 51, 10 = 1 + 24/60 + 51/60×60 + 10/60x60x60.

for further study refer: http://it.stlawu.edu/~dmelvill.....C7289.html

It is the ‘sexagesimal Babylonian cuneiform system’ depicted in the face of a clay tablet from the Yale Babylonian Collection (7289).

Across the diagonal is written 1 24 51 10 = 1 + 24/60 + 51/3600 + 10/216000, which is 1.41421296 to 9 significant decimal figures. The true 9-figure approximation to the square root of 2 is 1.41421356! The 30 at upper left presumably represents a somewhat arbitrary dimension assigned to the side of the square. The length of the diagonal, on this assumption, is 30 times the square root of 2, which is 45 25 35 in base 60.

Thus,the Babylonians knew that the ratio of diagonal to side was exactly the square root of 2.

This is the root(2) tablet from the Yale Babylonian Collection found near the Euphrates River dating from around 2000 B.C.

Babylonian clay tablet, with annotations in Cuneiform script…The diagonal displays an approximation of the square root of 2

1 + 24/60 + 51/(60*60) + 10/(60*60*60) = 1.41421….

This is the Babylonian Clay Tablet ( YBC 7289).

Its claim to fame is the fact that it is the world’s first representation of sexagesimal approximation of the number “square root of 2”- the length of the diagonal of a unit square.This has wide reaching consequences, in the field of Numerical analysis, used nowadays for example : Stock markets

regards,

Tathagata Chatterjee

its the yale tablet YBC-7289…The famous ‘root(2)’ tablet from the Yale Babylonian Collection.significance:the Babylonians found this remarkably good approximation to √2.it also proves dat babylonians knew about pythagores theorem.

The famous ‘root(2)’ tablet from the Yale Babylonian Collection.

[wiki rip]

Babylonian clay tablet YBC 7289 with annotations. The diagonal displays an approximation of the square root of 2 in four sexagesimal figures, which is about six decimal figures.

1 + 24/60 + 51/602 + 10/603 = 1.41421296…

(Image by Bill Casselman)

[/wiki rip]

Rivers of Babylon!

The picture is that of a clay tablet recovered from excavations of the sites of ancient babylonian civilizations.

The tablet describes base-60 mathematics, the base from which current time is derived.

The numbers “1 24 51 10” indicate the square root of 2 in base-60

The numbers 42, 25 and 35 are the lengths of the sides of a square as marked. After appropriate conversions, the length of the diagonal is ~ 1.414, which is root 2. And this was some years before pythagoras! The numbers are more appropriately called Babylonian Pythagorean Triplets

For those interested in reading Babylonian mathematical tablets: http://www.math.ubc.ca/~cass/c......html#read