Due to some errors in the table and damage to the tablet, variant, interpretations, still related to right triangles, are possible.

Neugebauer and Sachs saw Plimpton 322 as a study of solutions to the Pythagorean equation in whole numbers, and suggested a number-theoretic motivation.

The proposal that Plimpton 322 is a trigonometric table is ruled out for similar reasons, given that the Babylonians appear not to have had the concept of angle measure.

Various proposals have been made, including that the tablet had some practical purpose in architecture or surveying, that it was geometrical investigation motivated by mathematical interest, or that it was compilation of parameters to enable a teacher to set problems for students.

With regard to the latter proposal, Creighton Buck, reporting on never-published work of D. L. Voils, raises the possibility that the tablet may have only an incidental relation to right triangles, its primary purpose being to help set problems relating to reciprocal pairs, akin to modern day quadratic-equation problems.

Other scholars, such as Jöran Friberg and Eleanor Robson, who also favor the teacher's aid interpretation, state that the intended problems probably did relate to right triangles.

According to Banks, the tablet came from Senkereh, a site in southern Iraq corresponding to the ancient city of Larsa.

More specifically, based on formatting similarities with other tablets from Larsa that have explicit dates written on them, Plimpton 322 might well be from the period 1822–1784 BC.

[9] The main content of Plimpton 322 is a table of numbers, with four columns and fifteen rows, in Babylonian sexagesimal notation.

Similarly Britton, Proust & Shnider (2011) (p. 526) observe that the term often appears in the problems where completing the square is used to solve what would now be understood as quadratic equations, in which context it refers to the side of the completed square, but that it might also serve to indicate "that a linear dimension or line segment is meant".Neugebauer & Sachs (1945) (pp.

35, 39), on the other hand, exhibit instances where the term refers to outcomes of a wide variety of different mathematical operations and propose the translation "'solving number of the width (or the diagonal).'"

Neugebauer & Sachs (1945) reconstructed the first word as takilti (a form of takiltum), a reading that has been accepted by most subsequent researchers.

The heading was generally regarded as untranslatable until Robson (2001) proposed inserting a 1 in the broken-off part of line 2 and succeeded in deciphering the illegible final word, producing the reading given in the table above.

While they note that, in almost all cases, it refers to the linear dimension of the auxiliary square added to a figure in the process of completing the square, and is the quantity subtracted in the last step of solving a quadratic, they agree with Robson that in this instance it is to be understood as referring to the area of a square.Friberg (2007), on the other hand, proposes that in the broken-off portion of the heading takiltum may have been preceded by a-ša ("area").

The error in Row 8, Column 1 (replacing the two sexagesimal digits 45 14 by their sum, 59) appears not to have been noticed in some of the early papers on the tablet.

It has sometimes been regarded (for example in Robson (2001)) as a simple mistake made by the scribe in the process of copying from a work tablet.

Robson also argues that the proposal does not explain how the errors in the table could have plausibly arisen and is not in keeping with the mathematical culture of the time.

The multiplier a used to compute the values in columns 2 and 3, which can be thought of as a rescaling of the side lengths, arises from application of the "trailing part algorithm", in which both values are repeatedly multiplied by the reciprocal of any regular factor common to the last sexagesimal digits of both, until no such common factor remains.

Jöran Friberg translated and analyzed the two tablets and discovered that both contain examples of the calculation of the diagonal and side lengths of a rectangle using reciprocal pairs as the starting point.

The parameters of MS 3971 do, however, all correspond to rows of de Solla Price's proposed extension of the table of Plimpton 322, also discussed below.

Neugebauer and Sachs had, in fact, noted the possibility of using reciprocal pairs in their original work, and rejected it for this reason.

It was observed by de Solla Price (1964), working within the generating-pair framework, that every row of the table is generated by a q that satisfies 1 ≤ q<60, that is, that q is always a single-digit sexagesimal number.

Furthermore, there are exactly 15 regular ratios between 9/5 and 12/5 inclusive for which q is a single-digit sexagesimal number, and these are in one-to-one correspondence with the rows of the tablet.

He notes that the vertical scoring between columns on the tablet has been continued onto the back, suggesting that the scribe might have intended to extend the table.

She admits the "shockingly ad hoc" nature of this scheme, which serves mainly as a rhetorical device for criticizing all attempts at divining the selection criteria of the tablet's author.

[28] Otto E. Neugebauer (1957) argued for a number-theoretic interpretation, but also believed that the entries in the table were the result of a deliberate selection process aimed at achieving the fairly regular decrease of the values in Column 1 within some specified bounds.

Buck (1980) and Robson (2002) both mention the existence of a trigonometric explanation, which Robson attributes to the authors of various general histories and unpublished works, but which may derive from the observation in Neugebauer & Sachs (1945) that the values of the first column can be interpreted as the squared secant or tangent (depending on the missing digit) of the angle opposite the short side of the right triangle described by each row, and the rows are sorted by these angles in roughly one-degree increments.

Consequently, the square root of the number (minus the one) in the first column is what we would today call the tangent of the angle opposite the short side.

"[30] Robson argues on linguistic grounds that the trigonometric theory is "conceptually anachronistic": it depends on too many other ideas not present in the record of Babylonian mathematics from that time.

It makes use of mathematical methods typical of scribal schools of the time, and it is written in a document format used by administrators in that period.