Plimpton 322: A Study of Rectangles

Mansfield, Daniel F.

doi:10.1007/s10699-021-09806-0

Cited by 6 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For 5 n = we get the following estimates from the standard and improved series 1 serves credit for enormously improving a practically useless series expansion of (7).…”

Section: Series Expansions For Estimating πmentioning

confidence: 99%

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet

Beji¹

2022

APM

View full text Add to dashboard Cite

A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calculations. The approach is classical but the formulation of coupled recursion relations is new. Further, use of infinite series for computing π is explored by an improved version of Leibniz's series expansion. Finally, some remarks with reference to π are made on a relatively recently rediscovered Sumerian tablet depicting geometric figures.

show abstract

“…For 5 n = we get the following estimates from the standard and improved series 1 serves credit for enormously improving a practically useless series expansion of (7).…”

Section: Series Expansions For Estimating πmentioning

confidence: 99%

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet

Beji¹

2022

APM

View full text Add to dashboard Cite

show abstract

“…Pythagorean triples appeared in Babylonians tablets. The most famous is Plimpton 322 [31,21]. An other one is Si.427.…”

Section: Babylonian Triplets and Pythagorasmentioning

confidence: 99%

“…To cite [31] about research theories in history: "In general, we can say that the successful theory [in the history of mathematics] should not only be mathematically valid but historically, archaeologically, and linguistically sensitive too." [21] for example has produced the 2021 controversy: the paper has been picked up by media. Math historian Victor Blasjö formulated it nicely: 'it tricked news outlets into printing nonsense headlines".…”

Section: Babylonian Triplets and Pythagorasmentioning

confidence: 99%

The Babylonian Graph

Knill¹

2022

Preprint

View full text Add to dashboard Cite

The Babylonian graph B has the positive integers as vertices and connects two if they define a Pythagorean triple. Triangular subgraphs correspond to Euler bricks. What are the properties of this graph? Are there tetrahedral subgraphs corresponding to Euler tesseracts? Is there only one infinite connected component? Are there two Euler bricks in the graph that are disconnected? Do the number of edges or triangles in the subgraph generated by the first n vertices grow like of the order n W(n), where n is the product log? We prove here some simple results. In an appendix, we include handout from a talk on Euler cuboids given in the year 2009.

show abstract

The Role of History in Enriching Mathematics Teachers’ Training for Primary Education (6–12 Years Old Students)

Vanegas

Giménez

Prat

2023

Advances in Mathematics Education

View full text Add to dashboard Cite

Plimpton 322: A Study of Rectangles

Abstract: Plimpton 322 is one of the most sophisticated and interesting mathematical objects from antiquity. It is often regarded as teacher’s list of school problems, however new analysis suggests that it relates to a particular geometric problem in contemporary surveying.

Cited by 6 publications

References 18 publications

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet

The Babylonian Graph

The Role of History in Enriching Mathematics Teachers’ Training for Primary Education (6–12 Years Old Students)

Contact Info

Product

Resources

About

Plimpton 322: A Study of Rectangles

Abstract: Plimpton 322 is one of the most sophisticated and interesting mathematical objects from antiquity. It is often regarded as teacher’s list of school problems, however new analysis suggests that it relates to a particular geometric problem in contemporary surveying.

Cited by 6 publications

References 18 publications

A Geometric Formulation and a Series Approach for Estimating &lt;i&gt;π&lt;/i&gt; with Remarks on a Sumerian Tablet

A Geometric Formulation and a Series Approach for Estimating &lt;i&gt;π&lt;/i&gt; with Remarks on a Sumerian Tablet

The Babylonian Graph

The Role of History in Enriching Mathematics Teachers’ Training for Primary Education (6–12 Years Old Students)

Contact Info

Product

Resources

About

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet

A Geometric Formulation and a Series Approach for Estimating <i>π</i> with Remarks on a Sumerian Tablet