View Full Version : Babylonian scholars may have invented Trigonometry

shunyadragon

08-27-2017, 05:55 PM

An ancient clay tablet shows that Babylonian scholars might have invented trigonometry

A new interpretation into the nature of an ancient clay tablet known as Plimpton 322 claims that ancient Babylonians might have developed an advanced form of trigonometry — long before Greek mathematicians are commonly believed to have invented the concept.

That’s the theory put forward by two mathematicians from the University of New South Wales, Daniel F. Mansfield and Norman Wildberger, who published their study in the latest issue of Historia Mathematica. They claim that the tablet demonstrates a sophisticated understanding of mathematics, and that modern assumptions of the field should be reexamined in light of the interpretation.

The tablet in question is approximately five inches wide by three inch tall, and dates back to somewhere between 1822 and 1762 BCE. It was discovered by an American archeologist and diplomat named Edgar Banks in Larsa (what is now in southern Iraq) in the early 1920s. Banks sold the tablet to New York publisher George Arthur Plimpton, who later bequeathed it and his collection to Columbia University.

Teallaura

08-27-2017, 06:29 PM

Yeah, I saw that the other day - I'm still ticked off at those guys for not being around when I had to take trig!

shunyadragon

08-27-2017, 07:03 PM

Yeah, I saw that the other day - I'm still ticked off at those guys for not being around when I had to take trig!

You just needed to learn base 60 math, and it would be easy as pie!

Raphael

08-27-2017, 07:12 PM

So now we know who to blame.

KingsGambit

08-27-2017, 07:15 PM

So now we know who to blame.

I actually enjoyed studying trig and calculus.

rogue06

08-27-2017, 08:40 PM

An ancient clay tablet shows that Babylonian scholars might have invented trigonometry

A new interpretation into the nature of an ancient clay tablet known as Plimpton 322 claims that ancient Babylonians might have developed an advanced form of trigonometry — long before Greek mathematicians are commonly believed to have invented the concept.

That’s the theory put forward by two mathematicians from the University of New South Wales, Daniel F. Mansfield and Norman Wildberger, who published their study in the latest issue of Historia Mathematica. They claim that the tablet demonstrates a sophisticated understanding of mathematics, and that modern assumptions of the field should be reexamined in light of the interpretation.

The tablet in question is approximately five inches wide by three inch tall, and dates back to somewhere between 1822 and 1762 BCE. It was discovered by an American archeologist and diplomat named Edgar Banks in Larsa (what is now in southern Iraq) in the early 1920s. Banks sold the tablet to New York publisher George Arthur Plimpton, who later bequeathed it and his collection to Columbia University.

That the ancient Babylonians knew of and employed some of the concepts of trigonometry is nothing new. See for example The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph not to mention it has long been suspected that the Babylonian clay tablet known as Plimpton 322 contains a trigonometrical table since R. Creighton Buck brought it up in 1980.

Jedidiah

08-27-2017, 09:26 PM

Yeah, I saw that the other day - I'm still ticked off at those guys for not being around when I had to take trig!

I loved trig and I used it a a surveyor.

Sparko

08-28-2017, 05:19 AM

23853

shunyadragon

08-28-2017, 06:22 AM

That the ancient Babylonians knew of and employed some of the concepts of trigonometry is nothing new. See for example The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph not to mention it has long been suspected that the Babylonian clay tablet known as Plimpton 322 contains a trigonometrical table since R. Creighton Buck brought it up in 1980.

The point of the article is that there is a more complete translation of tablet providing more details of the Babylonian knowledge of trigonometry. Yes, there is a bit of hype here, but nonetheless the improved translation showed how the Babylonian math developed trigonometry.

Most likely trigonometry and the similar math of early cultures developed over time through the engineering of their building methods.

Raphael

08-28-2017, 04:51 PM

23853

that image is seriously messing with the migraine I currently have.

37818

08-29-2017, 06:35 AM

Just yesterday (8-28) on a radio talk show (Larry Elder) a guest mathematician Martin Magid, a professor of mathematics at Wellesley College, explained that the Babylonian clay tablet used what we call Pythagorean triples and a base 60 numbering system. That is what I had understood.

An image of the tablet. 23867

37818

08-29-2017, 12:07 PM

Here is a link to a PDF about the tablet:

http://www.sciencedirect.com/science/article/pii/S0315086001923171/pdf?md5=9ceef9ced7e930ed510664744b42da42&pid=1-s2.0-S0315086001923171-main.pdf&_valck=1

Sparko

08-29-2017, 12:10 PM

Just yesterday (8-28) on a radio talk show (Larry Elder) a guest mathematician Martin Magid, a professor of mathematics at Wellesley College, explained that the Babylonian clay tablet used what we call Pythagorean triples and a base 60 numbering system. That is what I had understood.

An image of the tablet. 23867

It's like a Flintstone spreadsheet.

37818

08-29-2017, 12:17 PM

It's like a Flintstone spreadsheet.

Yeah. And it is not trig. It is a table of what we think of as Pythagorean triples but 100's of years before Pythagoras.

shunyadragon

08-29-2017, 01:09 PM

Yeah. And it is not trig. It is a table of what we think of as Pythagorean triples but 100's of years before Pythagoras.

It is generally accepted as primitive form of trig, probably developed in engineering buildings.

37818

08-29-2017, 02:12 PM

It is generally accepted as primitive form of trig, probably developed in engineering buildings.

Read the PDF. Its author claims, "I show that the popular view of it as some sort of trigonometric table cannot be correct."

Teallaura

09-02-2017, 02:26 PM

UPI did a pretty good job explaining it.

https://www.upi.com/Science_News/2017/08/25/Worlds-first-trigonometry-revealed-in-ancient-Babylonian-tablet/2181503668755/

Who knew UPI was still in business? :shrug:

37818

09-27-2017, 06:41 AM

Pythagorean triples can be easily calculated.

Side A being the short leg of the right triangle. Side B being the long leg. Side C being the hypotenuse, side opposite the right angle.

Pythagorean theorem being A2 + B2 = C2

Where the integer difference between C - B = n. Were A / n => an integer value of 2. And A and n must both be either odd or even.

(A2 - n2) / ( 2 x n) = B and B + n = C.

So if we make A = 9 and n = 1.

B = 40 and C = 41.

shunyadragon

09-30-2017, 09:54 AM

Pythagorean triples can be easily calculated.

Side A being the short leg of the right triangle. Side B being the long leg. Side C being the hypotenuse, side opposite the right angle.

Pythagorean theorem being A2 + B2 = C2

Where the integer difference between C - B = n. Were A / n => an integer value of 2. And A and n must both be either odd or even.

(A2 - n2) / ( 2 x n) = B and B + n = C.

So if we make A = 9 and n = 1.

B = 40 and C = 41.

True in today' math, but what's the point?

37818

10-12-2017, 06:18 AM

True in today' math, but what's the point?

No reason other than . . . . The tablet has a table of triangle triples. And I remembered having stumbling upon an easy way to calculate such triples.

Powered by vBulletin® Version 4.2.5 Copyright © 2019 vBulletin Solutions Inc. All rights reserved.