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## Who discovered linear equation?

Asked by anonymous -

This question can also be asked as:

### who discovered equations for area and volume?

### what is the purpose of matrices?

# Highest Rated Answer

Linear algebra -

The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.

Matrices were poorly-defined before the development of ring theory within abstract algebra. With the coming of special relativity, many practitioners gained appreciation of the subtleties of linear algebra. Furthermore, the routine application of Cramer's rule to solve partial differential equations led to the inclusion of linear algebra in standard coursework at universities. E.T. Copson wrote, for instance,

? When I went to Edinburgh as a young lecturer in 1922, I was surprised to find how different the curriculum was from that at Oxford. It included topics such as Lebesgue integration, matrix theory, numerical analysis, Riemannian geometry, of which I knew nothing... ?

?E.T. Copson, Preface to Partial Differential Equations, 1973

Francis Galton initiated the use of correlation coefficients in 1888. Often more than one random variable is in play and may be cross-correlated. In statistical analysis of multivariate random variables the correlation matrix is a natural tool. Thus, statistical study of such random vectors helped establish matrix usage.

http://en.wikipedia.org/wiki/Linear_algebra

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Pythagorean theorem

In mathematics, the Pythagorean theorem (American English) or Pythagoras' theorem (British English) is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although knowledge of the theorem almost certainly predates him.

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

The theorem is as follows:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

This is usually summarized as:

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

http://en.wikipedia.org/wiki/Pythagorean_theorem

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With regard to length, area, and volume, teachers should know what is meant by one, two, and three dimensions.

(A common misunderstanding: perimeter is two dimensional since, after all, "the perimeter of a rectangle has both length and width.")

Many teachers who know the formula A = L W may have no grasp of how the linear units of a rectangle's length and width are related to the units that measure its area or why multiplying linear dimensions yields the count of those units.

An understanding of the volume of a rectangular solid involves seeing the relationship between layers of three-dimensional units and the area of its base.

Formulas for the area and volume of some other kinds of objects can build from an understanding of rectangles and rectangular solids.

The study of rectangles and rectangular solids can also lead to an understanding of how length, area, and volume change under uniform dilation.

http://www.cbmsweb.org/MET_Document/index.htm

# Other Answers

Linear equations are a part of number theory, the earliest examples are found in India. They were interested in finding integral solutions of Diophantine equations. No one person can claim to be the discoverer of them.

For more information see: http://en.wikipedia.org/wiki/Number_theory