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Who Invented Trigonometry?

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    Posted: 31-Mar-2006 at 09:41

I'm not that fond of Trigonometry but want to know this question.

Who Invented Trigonometry?

For those of you who do not know what Trigonometry looks like.....here are some pictures.

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  Quote hugoestr Quote  Post ReplyReply Direct Link To This Post Posted: 31-Mar-2006 at 10:43
Trig was not invented, but discovered.
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  Quote Questions! Quote  Post ReplyReply Direct Link To This Post Posted: 31-Mar-2006 at 10:47

Originally posted by hugoestr

Trig was not invented, but discovered.

By whom and where?

 

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  Quote Anujkhamar Quote  Post ReplyReply Direct Link To This Post Posted: 31-Mar-2006 at 12:51
Greeks claim the word trigonometry comes from the ancient greek word trigonon (3 angles).

Indians claim the word came from a word in sanskrit.

It sprung up all over the world at around the same period in Mesopotamia, India and Egypt, which are all responsible for developing different ideas of it. No one person can be said to have discovered it, however many have developed it over time. For more info:

http://en.wikipedia.org/wiki/Trigonometry
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  Quote Leonardo Quote  Post ReplyReply Direct Link To This Post Posted: 31-Mar-2006 at 13:00

It's impossible to name a single person. Some theorems that we now call "trigonometry" can be found in the works of ancient mathematicians of the hellenist period (Euclid, Aristarcus, Archimedes and others) and perhaps also in some "mathematical" tablets written by ancient Mesopotamians.

It's generally accepted by historians that the first person who wrote trigonometrical tables was the famous astronomer Hipparcus. His table of the "chords" survives in the Almagest, the famous work of the astronomer Ptolomeus (who lived centuries after Hipparchus). Ancient Indian mathematicians are generally recognized as the first who introduced what we now call "sine function". The Arabs then spread this novelty in the islamic world and also in Europe.

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  Quote Jhuntadu Quote  Post ReplyReply Direct Link To This Post Posted: 31-Mar-2006 at 18:47

So is it true that Pythagoras discovered what we know as Pythagoras theorem.

HAPPY ALL FOOL'S DAY
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  Quote Leonardo Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 02:26
Originally posted by Jhuntadu

So is it true that Pythagoras discovered what we know as Pythagoras theorem.

 

Well, there are two ways one can think at Mathematics: the first considers Maths as a logical system based on axioms/postulates and theorems, the second as a set of practical/pragmatic knowledges on the properties of numbers and figures.

In western countries, following the model of The Elements of Euclid, geometry is teached (or perhaps was teached for centuries   ) as a logical system of theorems deduced from a set of axioms (the axioms of euclidean geometry), and so only here we can talk properly of "Pythagoras' theorem".

It's well known that a practical knowledge of what we call "Pythagoras' theorem" was shared by ancient Mesopotamians, ancient Indians and also ancient Chinese, but before their contact with models based on ancient Greek sources (mediated by the Arabs) they never developped a fully logical and coherent system of theorems based on axioms.

So we can conclude that before ancient Greek mathematicians there was a notable knowledge of properties of triangles but there were not "theorems" of any sort.



Edited by Leonardo
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  Quote Anujkhamar Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 04:31
I am curious to know whether if it was the other way round would the Greeks still claim "pythagoras's theorem"

Edited by Anujkhamar
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  Quote Leonardo Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 04:43

Originally posted by Anujkhamar

I am curious to know whether if it was the other way round would the Greeks still claim "pythagoras's formula"

A formula is not a theorem

 

 

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  Quote Questions Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 06:01
Originally posted by Leonardo

Originally posted by Anujkhamar

I am curious to know whether if it was the other way round would the Greeks still claim "pythagoras's formula"

A formula is not a theorem

& both...a theorem & it's inverse are correct/true?

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  Quote Anujkhamar Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 06:19
sorry typo

edited

to elborate imagine this scenario:

Ancient Greeks, such as Pythagoras, had the practical knowledge of Phythagorus's theorem. Aryabhatta then used "a logical system of theorems deduced from a set of axioms".

The chances are, it would still be known as "Pythagoras's theorem" and the Greeks would argue that as they had the practical knowledge it should be known as theirs. Then western philosophers would back their claim.

It's funny how the human mind works


Edited by Anujkhamar
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  Quote Questions! Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 08:18

Originally posted by hugoestr

Trig was not invented, but discovered.

So the question my dear comrades,ladies and gentlemen still remains a question?If I had a million dollars I would have turned it into a million dollar question,if I was sure about the existence of my soul....I would have sold it in order to find the correct answer.

Who Invented/Discovered TRIGONOMETRY and when?

Herez a poem to lighten your mood....

Trigonometry

Trigonometry began
When Sine and Cos and Tan
[The latter, a perfect gentleman]
Agreed to work in a Triangle.

Now Sine was cross with Cos
Because she got into a tangle
With Cosec the Smart Alec,
Who had a special angle

For flirty Cotangent
[Also known as Cot]
Whose reputation
[Or shall we say, computation? ]
Was certainly not

Above board, like Tangent
[Also known as Tan,
Who, I repeat, was a perfect gentleman]

Cross-fighting in the Triangle,
They drew an obtuse angle;
And slowly by degrees
Sine began to freeze

Till one fine day,
Cosec ran away
With Cotangent...
Which left a place vacant
For the incorrigible Secant,
Who fought and fell out with Tangent

In short,
Thanks to Cosec and Cot,
Trigonometry
Had to be abandoned.

Tan Pratonix

and the link to the poem is here ----------------->

http://www.poemhunter.com/p/m/poem.asppoet=138033&poem=2 505277

and the question is still waiting for it's mate?

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  Quote Leonardo Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 08:23

Originally posted by Anujkhamar

sorry typo

edited

to elborate imagine this scenario:

Ancient Greeks, such as Pythagoras, had the practical knowledge of Phythagorus's theorem. Aryabhatta then used "a logical system of theorems deduced from a set of axioms".

The chances are, it would still be known as "Pythagoras's theorem" and the Greeks would argue that as they had the practical knowledge it should be known as theirs. Then western philosophers would back their claim.

It's funny how the human mind works

 

Yes, it's funny and I partly agree with you

You probably know that Pythagoras is a semilegendary figure. No one historian really believes that the "historical" Pythagoras demonstrated the theorem that brings his name, at least not in the sense that we use following Aristoteles and Euclid.

"Pythagoras theorem" is only a conventional term, probably introduced by the philosopher Proclus, who lived centuries after Pythagoras, indicating the proposition 47 of the Book I of the Elements of Euclid (300 B.C.): "In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle".

You are right, at the time of Pythagoras the Greeks had only practical knowledge on geometry, the same that they inherited from other more ancient civilizations (Mesopotamians, Egyptians, maybe also Indians), but at the time of Euclid the hellenistic world developped what we still today call "mathematics" in the modern sense: a fully logical-deductive system based on axioms and theorems. Other civilizations, who came after inherited from hellenistic world this kind of maths (the Arabs for example).

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  Quote Question Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 08:26
Originally posted by Leonardo

Yes, it's funny and I partly agree with you

You probably know that Pythagoras is a semilegendary figure. No one historian really believes that the "historical" Pythagoras demonstrated the theorem that brings his name, at least not in the sense that we use following Aristoteles and Euclid.

I agree fully with you Leonardo.Now let's see what our Greek friends have to say on this question.Would you like to invite them to this question.You live in their vicinity.

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  Quote Question Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 08:38

Hi Leonardo I didn't mean the actual Greeks.Alpha to Omega of western civilization.Anyone who is interested in this topic is welcome.I believe in open discussions.

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  Quote Question Quote  Post ReplyReply Direct Link To This Post Posted: 01-Apr-2006 at 21:43

Did Pythagoras discover the Pythagoras Theorem.

Kindly take a look at this article.

The statement of the Theorem was discovered on a Babylonian tablet circa 1900-1600 B.C. Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. Euclid's (c 300 B.C.) Elements furnish the first and, later, the standard reference in Geometry. In fact Euclid supplied two very different proofs: the Proposition I.47 (First Book, Proposition 47) and VI.31. The Theorem is reversible which means that a triangle whose sides satisfy a2 + b2 = c2 is necessarily right angled. Euclid was the first (I.48) to mention and prove this fact.

http://www.cut-the-knot.org/pythagoras/index.shtml

Any comments?

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  Quote Aurelia Quote  Post ReplyReply Direct Link To This Post Posted: 04-Apr-2006 at 09:26
Themes > Science > Mathematics > Trigonometry > History

The history of trigonometry goes back to the earliest recorded mathematics in Egypt and Babylon. The Babylonians established the measurement of angles in degrees, minutes, and seconds. Not until the time of the Greeks, however, did any considerable amount of trigonometry exist. In the 2nd century BC the astronomer Hipparchus compiled a trigonometric table for solving triangles. Starting with 71 and going up to 180 by steps of 71, the table gave for each angle the length of the chord subtending that angle in a circle of a fixed radius r. Such a table is equivalent to a sine table. The value that Hipparchus used for r is not certain, but 300 years later the astronomer Ptolemy used r = 60 because the Hellenistic Greeks had adopted the Babylonian base-60 (sexagesimal) numeration system.
In his great astronomical handbook, The Almagest, Ptolemy provided a table of chords for steps of 1, from 0 to 180, that is accurate to 1/3600 of a unit. He also explained his method for constructing his table of chords, and in the course of the book he gave many examples of how to use the table to find unknown parts of triangles from known parts. Ptolemy provided what is now known as Menelaus's theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. At perhaps the same time as Ptolemy, however, Indian astronomers had developed a trigonometric system based on the sine function rather than the chord function of the Greeks. This sine function, unlike the modern one, was not a ratio but simply the length of the side opposite the angle in a right triangle of fixed hypotenuse. The Indians used various values for the hypotenuse.
Late in the 8th century, Muslim astronomers inherited both the Greek and the Indian traditions, but they seem to have preferred the sine function. By the end of the 10th century they had completed the sine and the five other functions and had discovered and proved several basic theorems of trigonometry for both plane and spherical triangles. Several mathematicians suggested using r = 1 instead of r = 60; this exactly produces the modern values of the trigonometric functions. The Muslims also introduced the polar triangle for spherical triangles. All of these discoveries were applied both for astronomical purposes and as an aid in astronomical time-keeping and in finding the direction of Mecca for the five daily prayers required by Muslim law. Muslim scientists also produced tables of great precision. For example, their tables of the sine and tangent, constructed for steps of 1/60 of a degree, were accurate for better than one part in 700 million. Finally, the great astronomer Nasir ad-Din at- Tusi wrote the Book of the Transversal Figure, which was the first treatment of plane and spherical trigonometry as independent mathematical Science.
The Latin West became acquainted with Muslim trigonometry through translations of Arabic astronomy handbooks, beginning in the 12th century. The first major Western work on the subject was written by the German astronomer and mathematician Johann Mller, known as Regiomontanus. In the next century the German astronomer Georges Joachim, known as Rheticus introduced the modern conception of trigonometric functions as ratios instead of as the lengths of certain lines. The French mathematician Franois Vite introduced the polar triangle into spherical trigonometry, and stated the multiple-angle formulas for sin(nq) and cos(nq) in terms of the powers of sin(q) and cos(q).
Trigonometric calculations were greatly aided by the Scottish mathematician John Napier, who invented logarithms early in the 17th century. He also invented some memory aids for ten laws for solving spherical triangles, and some proportions (called Napier's analogies) for solving oblique spherical triangles.
Almost exactly one half century after Napier's publication of his logarithms, Isaac Newton invented the differential and integral calculus. One of the foundations of this work was Newton's representation of many functions as infinite series in the powers of x. Thus Newton found the series sin(x) and similar series for cos(x) and tan(x). With the invention of calculus, the trigonometric functions were taken over into analysis, where they still play important roles in both pure and applied mathematics.
Finally, in the 18th century the Swiss mathematician Leonhard Euler defined the trigonometric functions in terms of complex numbers (see Number). This made the whole subject of trigonometry just one of the many applications of complex numbers, and showed that the basic laws of trigonometry were simply consequences of the arithmetic of these numbers."

-from http://www.cartage.org.lb/en/themes/sciences/Mathematics/Tri gonometry/history/History%20.html

     
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  Quote TheAlaniDragonRising Quote  Post ReplyReply Direct Link To This Post Posted: 26-Jan-2012 at 17:11
This is incredibly interesting;

History topic: Pythagoras's theorem in Babylonian mathematics


Pythagoras's theorem in Babylonian mathematics

In this article we examine four Babylonian tablets which all have some connection with Pythagoras's theorem. Certainly the Babylonians were familiar with Pythagoras's theorem. A translation of a Babylonian tablet which is preserved in the British museum goes as follows:-

4 is the length and 5 the diagonal. What is the breadth ?
Its size is not known.
4 times 4 is 16.
5 times 5 is 25.
You take 16 from 25 and there remains 9.
What times what shall I take in order to get 9 ?
3 times 3 is 9.
3 is the breadth.

All the tablets we wish to consider in detail come from roughly the same period, namely that of the Old Babylonian Empire which flourished in Mesopotamia between 1900 BC and 1600 BC.


Here is a map of the region where the Babylonian civilisation flourished.

The article Babylonian mathematics gives some background to how the civilisation came about and the mathematical background which they inherited.

The four tablets which interest us here we will call the Yale tablet YBC 7289, Plimpton 322 (shown below), the Susa tablet, and the Tell Dhibayi tablet. Let us say a little about these tablets before describing the mathematics which they contain.

The Yale tablet YBC 7289 which we describe is one of a large collection of tablets held in the Yale Babylonian collection of Yale University. It consists of a tablet on which a diagram appears. The diagram is a square of side 30 with the diagonals drawn in. The tablet and its significance was first discussed in [5] and recently in [18].


Plimpton 322 is the tablet numbered 322 in the collection of G A Plimpton housed in Columbia University.

You can see from the picture that the top left hand corner of the tablet is damaged as and there is a large chip out of the tablet around the middle of the right hand side. Its date is not known accurately but it is put at between 1800 BC and 1650 BC. It is thought to be only part of a larger tablet, the remainder of which has been destroyed, and at first it was thought, as many such tablets are, to be a record of commercial transactions. However in [5] Neugebauer and Sachs gave a new interpretation and since then it has been the subject of a huge amount of interest.

The Susa tablet was discovered at the present town of Shush in the Khuzistan region of Iran. The town is about 350 km from the ancient city of Babylon. W K Loftus identified this as an important archaeological site as early as 1850 but excavations were not carried out until much later. The particular tablet which interests us here investigates how to calculate the radius of a circle through the vertices of an isosceles triangle.

Finally the Tell Dhibayi tablet was one of about 500 tablets found near Baghdad by archaeologists in 1962. Most relate to the administration of an ancient city which flourished in the time of Ibalpiel II of Eshunna and date from around 1750. The particular tablet which concerns us is not one relating to administration but one which presents a geometrical problem which asks for the dimensions of a rectangle whose area and diagonal are known.

Before looking at the mathematics contained in these four tablets we should say a little about their significance in understanding the scope of Babylonian mathematics. Firstly we should be careful not to read into early mathematics ideas which we can see clearly today yet which were never in the mind of the author. Conversely we must be careful not to underestimate the significance of the mathematics just because it has been produced by mathematicians who thought very differently from today's mathematicians. As a final comment on what these four tablets tell us of Babylonian mathematics we must be careful to realise that almost all of the mathematical achievements of the Babylonians, even if they were all recorded on clay tablets, will have been lost and even if these four may be seen as especially important among those surviving they may not represent the best of Babylonian mathematics.

There is no problem understanding what the Yale tablet YBC 7289 is about.


Here is a Diagram of Yale tablet

It has on it a diagram of a square with 30 on one side, the diagonals are drawn in and near the centre is written 1,24,51,10 and 42,25,35. Of course these numbers are written in Babylonian numerals to base 60. See our article on Babylonian numerals. Now the Babylonian numbers are always ambiguous and no indication occurs as to where the integer part ends and the fractional part begins. Assuming that the first number is 1; 24,51,10 then converting this to a decimal gives 1.414212963 while √2 = 1.414213562. Calculating 30 × [ 1;24,51,10 ] gives 42;25,35 which is the second number. The diagonal of a square of side 30 is found by multiplying 30 by the approximation to √2.

This shows a nice understanding of Pythagoras's theorem. However, even more significant is the question how the Babylonians found this remarkably good approximation to √2. Several authors, for example see [2] and [4], conjecture that the Babylonians used a method equivalent to Heron's method. The suggestion is that they started with a guess, say x. They then found e = x2 - 2 which is the error. Then

(x - e/2x)2 = x2 - e + (e/2x)2 = 2 + (e/2x)2

and they had a better approximation since if e is small then (e/2x)2 will be very small. Continuing the process with this better approximation to √2 yieds a still better approximation and so on. In fact as Joseph points out in [4], one needs only two steps of the algorithm if one starts with x = 1 to obtain the approximation 1;24,51,10.

This is certainly possible and the Babylonians' understanding of quadratics adds some weight to the claim. However there is no evidence of the algorithm being used in any other cases and its use here must remain no more than a fairly remote possibility. May I [EFR] suggest an alternative. The Babylonians produced tables of squares, in fact their whole understanding of multiplication was built round squares, so perhaps a more obvious approach for them would have been to make two guesses, one high and one low say a and b. Take their average (a + b)/2 and square it. If the square is greater than 2 then replace b by this better bound, while if the square is less than 2 then replace a by (a + b)/2. Continue with the algorithm.

Now this certainly takes many more steps to reach the sexagesimal approximation 1;24,51,10. In fact starting with a = 1 and b = 2 it takes 19 steps as the table below shows:


step decimal sexagesimal

1 1.500000000 1;29,59,59
2 1.250000000 1;14,59,59
3 1.375000000 1;22,29,59
4 1.437500000 1;26,14,59
5 1.406250000 1;24,22,29
6 1.421875000 1;25,18,44
7 1.414062500 1;24,50,37
8 1.417968750 1;25, 4,41
9 1.416015625 1;24,57,39
10 1.415039063 1;24,54, 8
11 1.414550781 1;24,52,22
12 1.414306641 1;24,51;30
13 1.414184570 1;24,51; 3
14 1.414245605 1;24,51;17
15 1.414215088 1;24,51;10
16 1.414199829 1;24,51; 7
17 1.414207458 1;24,51; 8
18 1.414211273 1;24,51; 9
19 1.414213181 1;24,51;10


However, the Babylonians were not frightened of computing and they may have been prepared to continue this straightforward calculation until the answer was correct to the third sexagesimal place.


Next we look again at Plimpton 322

The tablet has four columns with 15 rows. The last column is the simplest to understand for it gives the row number and so contains 1, 2, 3, ... , 15. The remarkable fact which Neugebauer and Sachs pointed out in [5] is that in every row the square of the number c in column 3 minus the square of the number b in column 2 is a perfect square, say h.

c2 - b2 = h2

So the table is a list of Pythagorean integer triples. Now this is not quite true since Neugebauer and Sachs believe that the scribe made four transcription errors, two in each column and this interpretation is required to make the rule work. The errors are readily seen to be genuine errors, however, for example 8,1 has been copied by the scribe as 9,1.

The first column is harder to understand, particularly since damage to the tablet means that part of it is missing. However, using the above notation, it is seen that the first column is just (c/h)2. Now so far so good, but if one were writing down Pythagorean triples one would find much easier ones than those which appear in the table. For example the Pythagorean triple 3, 4 , 5 does not appear neither does 5, 12, 13 and in fact the smallest Pythagorean triple which does appear is 45, 60, 75 (15 times 3, 4 , 5). Also the rows do not appear in any logical order except that the numbers in column 1 decrease regularly. The puzzle then is how the numbers were found and why are these particular Pythagorean triples are given in the table.

Several historians (see for example [2]) have suggested that column 1 is connected with the secant function. However, as Joseph comments [4]:-

This interpretation is a trifle fanciful.

Zeeman has made a fascinating observation. He has pointed out that if the Babylonians used the formulas h = 2mnb = m2-n2c = m2+n2 to generate Pythagorean triples then there are exactly 16 triples satisfying n ≤ 60, 30° ≤ t ≤ 45°, and tan2t = h2/b2 having a finite sexagesimal expansion (which is equivalent to mnb having 2, 3, and 5 as their only prime divisors). Now 15 of the 16 Pythagorean triples satisfying Zeeman's conditions appear in Plimpton 322. Is it the earliest known mathematical classification theorem? Although I cannot believe that Zeeman has it quite right, I do feel that his explanation must be on the right track.

To give a fair discussion of Plimpton 322 we should add that not all historians agree that this tablet concerns Pythagorean triples. For example Exarchakos, in [17], claims that the tablet is connected with the solution of quadratic equations and has nothing to do with Pythagorean triples:-

... we prove that in this tablet there is no evidence whatsoever that the Babylonians knew the Pythagorean theorem and the Pythagorean triads.

I feel that the arguments are weak, particularly since there are numerous tablets which show that the Babylonians of this period had a good understanding of Pythagoras's theorem. Other authors, although accepting that Plimpton 322 is a collection of Pythagorean triples, have argued that they had, as Viola writes in [31], a practical use in giving a:-

... general method for the approximate computation of areas of triangles.

The Susa tablet sets out a problem about an isosceles triangle with sides 50, 50 and 60. The problem is to find the radius of the circle through the three vertices.


Here is a Diagram of Susa tablet

Here we have labelled the triangle ABC and the centre of the circle is O. The perpendicular AD is drawn from A to meet the side BC. Now the triangle ABD is a right angled triangle so, using Pythagoras's theorem AD2 =AB2 - BD2, so AD = 40. Let the radius of the circle by x. Then AO = OB = x and OD = 40 - x. Using Pythagoras's theorem again on the triangle OBD we have

x2 = OD2 + DB2.

So

x2 = (40-x)2 + 302

giving x2 = 402 - 80x + x2 + 302

and so 80x = 2500 or, in sexagesimal, x = 31;15.

Finally consider the problem from the Tell Dhibayi tablet. It asks for the sides of a rectangle whose area is 0;45 and whose diagonal is 1;15. Now this to us is quite an easy exercise in solving equations. If the sides are xywe have xy = 0.75 and x2 + y2 = (1.25)2. We would substitute y = 0.75/x into the second equation to obtain a quadratic in x2 which is easily solved. This however is not the method of solution given by the Babylonians and really that is not surprising since it rests heavily on our algebraic understanding of equations. The way the Tell Dhibayi tablet solves the problem is, I would suggest, actually much more interesting than the modern method.

Here is the method from the Tell Dhibayi tablet. We preserve the modern notation x and y as each step for clarity but we do the calculations in sexagesimal notation (as of course does the tablet).

Compute 2xy = 1;30.

Subtract from x2 + y2 = 1;33,45 to get x2 + y2 - 2xy = 0;3,45.

Take the square root to obtain x - y = 0;15.

Divide by 2 to get (x - y)/2 = 0;7,30.

Divide x2 + y2 - 2xy = 0;3,45 by 4 to get x2/4 + y2/4 - xy/2 = 0;0,56,15.

Add xy = 0;45 to get x2/4 + y2/4 + xy/2 = 0;45,56,15.

Take the square root to obtain (x + y)/2 = 0;52,30.

Add (x + y)/2 = 0;52,30 to (x - y)/2 = 0;7,30 to get x = 1.

Subtract (x - y)/2 = 0;7,30 from (x + y)/2 = 0;52,30 to get y = 0;45.

Hence the rectangle has sides x = 1 and y = 0;45.

Is this not a beautiful piece of mathematics! Remember that it is 3750 years old. We should be grateful to the Babylonians for recording this little masterpiece on tablets of clay for us to appreciate today.

http://www-groups.dcs.st-and.ac.uk/~history/PrintHT/Babylonian_Pythagoras.html

What a handsome figure of a dragon. No wonder I fall madly in love with the Alani Dragon now, the avatar, it's a gorgeous dragon picture.
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Ron View Drop Down
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  Quote Ron Quote  Post ReplyReply Direct Link To This Post Posted: 29-Mar-2013 at 13:57
Dear Jhuntadu,
In Plato's book 'Meno' we can see an exact copy of the the second figure from the left on the cuneiform geometrical tablet you are showing us. I'm trying to find a connexion between the two. Can you tell me the name of the tablet and/or where I can find information especially about the texts written above and below? 
Thanks,
Ron.
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red clay View Drop Down
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  Quote red clay Quote  Post ReplyReply Direct Link To This Post Posted: 29-Mar-2013 at 18:09
Ron, the post you are responding to is 7 years old.  That member hasn't been active in years.  But possibly someone else can help.
"Arguing with someone who hates you or your ideas, is like playing chess with a pigeon. No matter what move you make, your opponent will walk all over the board and scramble the pieces".
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