Descartes
Descartes was the first mathematician to use the notation where the letters at the beginning of the alphabet represent data and the letters at the end of the alphabet to represent variables or unknowns.
Descartes’ understanding of algebra was deep. He stated that the number of distinct roots of an equation is equal to the degree of the equation. Descartes was willing to consider negative (he called them false roots) and imaginary roots. He developed a rule for determining the number of positive and negative roots in an equation. The Rule of Descartes as it is known states “An equation can have as many true [positive] roots as it contains changes of sign, from + to – or from – to +; and as many false [negative] roots as the number of times two + signs or two – signs are found in succession.”
Analytic Geometry
Descartes’ greatest contribution to mathematics was developing analytic geometry. The most basic definition of analytic geometry is applying algebra to geometry. Descartes established analytic geometry as “a way of visualizing algebraic formulas”. He developed the coordinate system as a “device to locate points on a plane”. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y-axis while the horizontal axis is designated as the x-axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from each axis the point lays. The position of the point in the coordinate system is specified by its two coordinates x and y. This is written as (x, y). The coordinate system is also known as the Cartesian coordinate system. The adjective Cartesian comes from Latin version of Rene Descartes’ name
The coordinate system was developed to locate points on a plane but it evolved into what we call analytic geometry. The fundamental principle of analytic geometry can be described as “all pairs of
Descartes’ understanding of algebra was deep. He stated that the number of distinct roots of an equation is equal to the degree of the equation. Descartes was willing to consider negative (he called them false roots) and imaginary roots. He developed a rule for determining the number of positive and negative roots in an equation. The Rule of Descartes as it is known states “An equation can have as many true [positive] roots as it contains changes of sign, from + to – or from – to +; and as many false [negative] roots as the number of times two + signs or two – signs are found in succession.”
Analytic Geometry
Descartes’ greatest contribution to mathematics was developing analytic geometry. The most basic definition of analytic geometry is applying algebra to geometry. Descartes established analytic geometry as “a way of visualizing algebraic formulas”. He developed the coordinate system as a “device to locate points on a plane”. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y-axis while the horizontal axis is designated as the x-axis. The intersection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from each axis the point lays. The position of the point in the coordinate system is specified by its two coordinates x and y. This is written as (x, y). The coordinate system is also known as the Cartesian coordinate system. The adjective Cartesian comes from Latin version of Rene Descartes’ name
The coordinate system was developed to locate points on a plane but it evolved into what we call analytic geometry. The fundamental principle of analytic geometry can be described as “all pairs of