Mathematical mystery of Babylonian tablet

[Frank_Hoenedge]

https://phys.org/news/2017-08-mathematical-mystery-ancient-babylonian-clay.html

UNSW Sydney scientists have discovered the purpose of a famous 3700-year old Babylonian clay tablet, revealing it is the world's oldest and most accurate trigonometric table, possibly used by ancient mathematical scribes to calculate how to construct palaces and temples and build canals.

The new research shows the Babylonians beat the Greeks to the invention of trigonometry - the study of triangles - by more than 1000 years, and reveals an ancient mathematical sophistication that had been hidden until now.

 

....A Pythagorean triple consists of three, positive whole numbers a, b and c such that a2 + b2 = c2. The integers 3, 4 and 5 are a well-known example of a Pythagorean triple, but the values on Plimpton 322 are often considerably larger with, for example, the first row referencing the triple 119, 120 and 169

 

[paperdyer]

19 hours ago, seanjo said:

Example please...i.e. fill in the letters with appropriate numbers....because (3x2) + (4x2) is not equal to 5x2!

Scratch that they are squared not multiplied by 2.

The "2" is supposed to be superscript to indicate "squared".  I wonder if the Babylonian's math was better than what we currently use?  Maybe we can get an exact number for Pi.  Also maybe they can show why 3 X 1/3 = 1 while 0.333333333...... X 3 doesn't.

[Calibeliever]

Very interesting.

[Frank_Hoenedge]

21 hours ago, seanjo said:

Example please...i.e. fill in the letters with appropriate numbers....because (3x2) + (4x2) is not equal to 5x2!

Scratch that they are squared not multiplied by 2.

Mate, it's a copy of the last paragraph of the article. Thanks though, it should say a^2 + b^2 = c^2

[paperdyer]

But since 0.3333333..............to infinity is the decimal version of 1/3 one can't be exact and the other exact since they are the same number.

[paperdyer]

4.  That just proves our math works right sometimes. Just trying to have a bit of fun with quirks of math.

[bison]

4 hours ago, paperdyer said:

The "2" is supposed to be superscript to indicate "squared".  I wonder if the Babylonian's math was better than what we currently use?  Maybe we can get an exact number for Pi.  Also maybe they can show why 3 X 1/3 = 1 while 0.333333333...... X 3 doesn't.

Sexagesimal numbers survive in our reckoning of angles: minutes, degrees, and seconds.  A full circle, 360 degrees, 0 minutes, 0 seconds, divided by the rather simple sexagesimal term  114  35  30 comes very very close to the Pi  ratio. Substantially fewer digits, it appears, than required to express Pi to a similar degree of precision in the decimal system.

Edited August 25, 2017 by bison

[jarjarbinks]

numbers are all made up from we invented them. that's why some people uses CM and others inches.
Imagine a system with PI=1.

[bison]

Pi is a ratio; one length compared to another. If you mean the circumference of a circle = 1, then the diameter is ~ 0.31831, which is 1 divided by Pi.

 

Edited August 25, 2017 by bison
added informaion

[pbarosso]

this makes perfect sense to me. this ratio based table would have been used to not only calculate the angle of the facing block when needed but also how tall and wide each step needs to be to keep a constant exact angle all the way up whther it be a smooth pyramid or facing OR steps.

[Unusual Tournament]

George the Greek, my local grocer is gonna be p***ed when i tell him this.

[Frank_Hoenedge]

Still a beauty as to how they found it, as an approach, to begin with

Edited August 26, 2017 by Frank_Hoenedge

[Ozymandias]

There are three ghings I love about thos story:

(1) the fact that Pythagoras' Theorem was known about more than 1000 years before Pyghagoras even lived;

(2) that the Babylonians were making quite accurate and exact calculations using their sexagesimal number system long before anyone else;

(3) their approach to trigonometry was entirely different from our modern one yet just as valid.

[Frank_Hoenedge]

Might even shed some kind of seasonal insight into the King's List, rather than an ascending chronology they might have had 'numerical compartments'.