Who Invented Trigonometry And What Is A Matrix In Math?
An ordered science named trigonometry was reconstructed by the ancient Greeks. Astronomy was the cause and motivation for the invention of trigonometry. The initial evolution of trigonometry was found in spherical trigonometry as its utilisation was significant in it. The answer to the question “Who invented trigonometry?” can be found in this article. Hipparchus, Ptolemy and Menelaus were the three important people who contributed to the development of trigonometry.
The need for a trigonometric table for the work in astronomy by Hipparchus led to a new invention of the construction of the table of chords. His theory states that “each triangle is being inscribed in the circle in a way that each side of it is a chord”.
The generalisation of the sun’s path being 360o was given by him and he further explained the division of the diameter into 120 pieces by indicating them as the sexagesimal fractions of the Babylonian type.
The book named “Sphaerica” authored by Menelaus from the three-book work discusses the concept of spherical trigonometry involving important details which helped to a greater extent in the evolution of trigonometry.
Ptolemy’s contribution to the field of trigonometry is vast. The table of chords was devised by him which is still prevalent and useful in the formulae of trigonometric functions.
The concept of a matrix was introduced by James Sylvester in the nineteenth century which provided the answer to the question “What is a matrix in math?”. The positioning of numbers in the form of rows and columns is a matrix. The rows are horizontal and the columns are vertical. Different operations can be performed on matrices. Every element of a matrix is represented with 2 subscripts. It explains the respective row and column to which the element belongs. The various types of matrices depending upon its order are square, diagonal, identity, symmetric, skew-symmetric, orthogonal, invertible, definite, triangular, row, column, singleton, null, non-singular, idempotent, scalar, equal, hermitian, involuntary, periodic and nilpotent matrix.
Few applications of matrices are given below:
- In the study of game theory and economics, the matrix of pay off explains the payoff of the two players.
- The concept of the adjacency matrix of a finite graph provides a foundation for the basic notion of graph theory.
- Markov chains with finitely many states are defined using the stochastic matrices. The square matrices consist of numbers which are positive and that sum up to 1 are stochastic matrices.
- The concept of linearly coupled harmonic systems is one of the main uses of matrices in physics.
- Matrix applications can be found in geometrical optics such as the equations of motion, force and mass matrix.
- Linear transformations and the symmetries associated with it play an important role in the field of modern physics.
- The idea of mesh analysis and nodal analysis in electronics give rise to a system of linear equations that can be explained with a matrix.
The uses of matrices have a long history. Few of them are listed above for reference.