Analytic geometry, well known also known as coordinate geometry or Cartesian geometry , is a scientific field in which algebraic symbolism and methods are used to represent and solve geometric problems. It establishes a co-relational relationship between geometric curves and algebraic equations.
This relationship enables it to reformulate problems in geometry as well as problems in algebra and the other way around, the methods of working of either subject can then be used to solve problems in the other. Apollonius of Perga, whose work inspired much of the development of analytic geometry for over 1800 years with his book, Conics, was known by his peers as The Great Geometer.
He referred a conic as the intersection of a cone and a plane. His treatise Conics is one of the greatest scientific works from the ancient world. In spite of Apollonius coming close to developing analytic geometry, he did not manage to do so because he did not take into account negative magnitudes and in every case, the coordinate system was superimposed upon a given curve a posteriori instead of a priori.
In other words, equations were determined by curves, but equations did not define curves. Coordinates, variables, and equations were subsidiary notions that were employed to a specific geometric situation.
The methods of analytic geometry have been comprehended to four or more dimensions and have been incorporated with other branches of geometry. When the 16th century was coming to an end, French mathematician Francois Viete developed the first systematic algebraic notation. Fermat and Rene Descartes then single-handedly founded analytic geometry in the 1630s by taking up Viete's algebra to the study of geometric loci.
Analytic geometry was founded in 1637 by René Descartes. It was of fundamental value in the development of the calculus by G. W. Leibniz and Sir Isaac Newton in the late 17th century. More recently it has served as the basis for the modern development and exploitation of algebraic geometry.
Analytic geometry represents objects using a coordinate system. It is profoundly used in fields such as science and engineering. The two-dimensional version of analytic geometry is often taught in secondary school algebra courses.
It shows x and y coordinates, representing horizontal and vertical movements, respectively. X and y coordinates are represented as an ordered pair. A fixed point located where x=6 and y=9 would be written as (6,9). Negative numbers refer to the left side of a plane for x and the bottom half for y. The axes meet at the origin, where both the x and y-axes converge, represented as (0,0).
3-D geometry integrates z-axis. The z-axis refers to vertical pair, and the y-axis is tipped over to embodied movement in the direction of and away from the viewer on a horizontal plane.
Its most regular application is in the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions.
For example, the linear equation ax + by + c =0 stands for a straight line in the XY -plane and the linear equation ax + by + cz + d =0 represents a plane in space, where a, b, c, and d are coefficients or in other terms, constants.
To this extent, a geometric problem can be furthered into an algebraic problem, and the methods of algebra brought to bear on its solution. On the contrary, the resolution of a problem in algebra, such as finding the roots of an equation or system of equations, can be approximated or given precisely by geometric means, for example, plotting curves and surfaces and determining points of intersections.
In-plane analytic geometry, a line is often described in terms of its slope (m). It expresses its inclination to the coordinate axes. Practically, the slope of a straight line is the trigonometric tangent of the angle it makes with the x-axis.
If the line is parallel to the x-axis, then its slope is zero. Two or more lines with equal slopes are said parallel to one another. In solid analytic geometry, the position of a straight line is given not by one slope but by its direction cosines, the cosines of the angles the line makes with the x-, y-, and z-axes.
Analytic geometry is undoubtedly a powerful tool important to computer graphics, including computer games. Coordinates are employed to place objects on the screen. It is significantly useful in the aircraft industry, especially when dealing with the shape of an airplane's fuselage.
In our day to day lives, analytical geometry is helpful for example if you wanted to measure the volume of a circle so that you could be aware beforehand if some liquid you tried to get into it would fit. In labs, geometry is applied for measurements of things as tiny as atoms or cells. For this and more info, you can seek for geometry help online by contacting us anytime for prompt assistance.