Linear algebra | Numerical linear algebra

Fangcheng (mathematics)

Fangcheng (sometimes written as fang-cheng or fang cheng) (Chinese: ๆ–น็จ‹; pinyin: fฤng chรฉng) is the title of the eighth chapter of the Chinese mathematical classic Jiuzhang suanshu (The Nine Chapters on the Mathematical Art) composed by several generations of scholars who flourished during the period from the 10th to the 2nd century BC. This text is one of the earliest surviving mathematical texts from China. Several historians of Chinese mathematics have observed that the term fangcheng is not easy to translate exactly. However, as a first approximation it has been translated as "rectangular arrays" or "square arrays". The term is also used to refer to a particular procedure for solving a certain class of problems discussed in Chapter 8 of The Nine Chapters book. The procedure referred to by the term fangcheng and explained in the eighth chapter of The Nine Chapters, is essentially a procedure to find the solution of systems of n equations in n unknowns and is equivalent to certain similar procedures in modern linear algebra. The earliest recorded fangcheng procedure is similar to what we now call Gaussian elimination. The fangcheng procedure was popular in ancient China and was transmitted to Japan. It is possible that this procedure was transmitted to Europe also and served as precursors of the modern theory of matrices, Gaussian elimination, and determinants. It is well known that there was not much work on linear algebra in Greece or Europe prior to Gottfried Leibniz's studies of elimination and determinants, beginning in 1678. Moreover, Leibniz was a Sinophile and was interested in the translations of such Chinese texts as were available to him. (Wikipedia).

Video thumbnail

Evaluate a linear expression for two variables

๐Ÿ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

Video thumbnail

What is the difference between finite and infinite sequences

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

What is the definition of an arithmetic sequence

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

What is the alternate in sign sequence

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

What is an arithmetic sequence

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

What is a sequence

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

Evaluating an expression with two variables ex 5, (bc)^2; b = 4; c = 8

๐Ÿ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

Video thumbnail

Evaluating a rational expression and order of operations

๐Ÿ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

Video thumbnail

What is the definition of a geometric sequence

๐Ÿ‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Video thumbnail

ICM 2006 Round Table

ICM 2006 Closing Round Table Are pure and applied mathematics drifting apart? Intervention by John Ball (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/table2006_ball.pdf) Intervention by Lennart Carleson (Slides https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/

From playlist Number Theory

Video thumbnail

On theories in mathematics education and their conceptual differences โ€“ Luis Radford โ€“ ICM2018

Mathematics Education and Popularization of Mathematics Invited Lecture 18.1 On theories in mathematics education and their conceptual differences Luis Radford Abstract: In this article I discuss some theories in mathematics education research. My goal is to highlight some of their diffe

From playlist Mathematics Education and Popularization of Mathematics

Video thumbnail

Lisa Rougetet - The Role of Mathematical Recreations in the 17th and 19th Centuries - CoM Apr 2021

The aim of this talk is to retrace the history of mathematical recreations since the first books entirely dedicated to them at the beginning of the 17th century and at the end of the 19th century, especially in Europe. I will explain what mathematical recreations were exactly when they fir

From playlist Celebration of Mind 2021

Video thumbnail

Does Math Reveal Reality?

Mathematics has an uncanny ability to describe the physical world. It elegantly explains and predicts features of space, time, matter, energy, and gravity. But is this magnificent scientific articulation an invention of the human mind or is mathematics indelibly imprinted upon the substrat

From playlist WSF Latest Releases

Video thumbnail

IMS Public Lecture: Foundations of Mathematics: An Optimistic Message

Stephen G. Simpson, Pennsylvania State University, USA

From playlist Public Lectures

Video thumbnail

Is Mathematics Invented or Discovered? | Episode 409 | Closer To Truth

Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans-like chisels and hammers and pieces of music? Or is mathematics discovered-always out there, somewhere, like mysterious islands waiting to be found? F

From playlist Closer To Truth | Season 4

Video thumbnail

CWM-CoD Joint Panel: Best practices towards a more diverse and inclusive mathematical community

Joint Panel organized by the IMU Committee for Women in Mathematics (CWM) and the IMU Committee on Diversity (CoD) CWM was established in 2015 to discuss issues related to women in mathematics worldwide and has actively worked to promote international contacts between national and region

From playlist IMU Live Events

Video thumbnail

Table ronde : mathรฉmatiques vivantes dans le monde

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Forum mathรฉmatiques vivantes

Video thumbnail

I still don't get it evaluating expressions

๐Ÿ‘‰ Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)

From playlist Simplify Expressions Using Order of Operations

Video thumbnail

Stephen Wolfram - Is Mathematics Invented or Discovered?

For more videos and information from Stephen Wolfram http://bit.ly/1GStsOr For more videos on whether mathematics is invented or discovered http://bit.ly/1DG70Hk To buy episodes and seasons of Closer To Truth click here http://bit.ly/1LUPlQS Mathematics describes the real world of atoms

From playlist Is Mathematics Invented or Discovered? - CTT Interview Series

Related pages

Yang Hui | Linear algebra | Determinant | Gaussian elimination | Matrix (mathematics) | Elimination theory | Indeterminate system