Geometry is essential for applied mathematics, and it is used in architecture and engineering fields. Its development was crucial in the development of modern mathematics. It can also make abstract mathematical concepts more clear.Continue Reading
Math is an abstract field, but it often must be used in physical objects. Geometry provides a means of applying mathematical ideas to construction, vehicles and virtually all objects. When studying how strong a building's support will be, architects must use geometric reasoning. Similarly, geometry allows airplane designers to measure how aerodynamic a particular design is.
Geometry was essential for developing modern mathematics. The ancient Greeks studied geometry extensively, and many modern algebra theorems and axioms have their roots in Greek geometry. The Greeks also used proofs with geometry, and their work allowed later Arabic mathematicians to develop algebra and algorithms. Algebra, and therefore all continuous mathematics, have strong ties to geometric concepts.
Understanding the natural world also requires an understanding of geometry. Fractals, which revolutionized mathematics in the 20th century, depend on simple geometric patterns that repeat themselves. The structure of trees, for example, can be described mathematically using fractal techniques. Fractal designs also have an influence on fields including art, cryptography, biology and artificial intelligence.Learn more about Geometry
The linear pair postulate is a mathematical concept used in conceptual geometry and engineering. It describes the relationship between two angles that form a linear pair, particularly when their values are added together, according to the Geometry Center at the University of Minnesota.Full Answer >
Of all the engineering disciplines, geometry is mostly used in civil engineering through surveying activities, explains TryEngineering.org. Geometry involves the analysis and study of relationships among shapes, and civil engineers design and assemble shapes to construct buildings, bridges, highway systems, tunnels, dams and other structures.Full Answer >
Spherical geometry is the branch of mathematics that deals with figures placed on the surface of a sphere. It can also be defined as a three-dimensional view of more traditional planar geometry; although, there are numerous differences between the planar and spherical subsets of geometrical study. Some of the basic tenets of planar geometry don't carry over to spherical geometry because it deals with different mathematical concepts.Full Answer >
Parallel lines are important in mathematics because they are at the base of several conjectures involving angles in geometry. Drawing a line, called a transversal, through a pair of parallel lines forms three different types of angles that have known mathematical properties.Full Answer >