Geometry

Geometry is a branch of mathematics concerned with questions of shape, size, and relative position of figures and the properties of space. Geometry is considered as one of the oldest mathematical sciences. The field of Astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems. A mathematician who works in the field of geometry is called a geometer.

The word Geometry is derived from the Greek word “Geos” meaning earth and “Metron” meaning measure. Geometry was very important to the ancient societies and was used for surveying, astronomy, navigation and building. Geometry also known Euclidean geometry which was written well over 2000 years ago in ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid and was called Elements, which has been used for over 2000 years.

Geometry is the study of angles and triangles, perimeter, area and volume as compared to algebra in which one develops a logical structure where mathematical relationships are provided and applied.

Practical Geometry

Geometry originated as a practical science concerned with surveying, measurements, areas and volumes. Among the notable accomplishments one finds formulas for lengths, areas and volumes, such as Pythagorean Theorem, circumference and area of a circle, triangle, and volume of a cylinder, sphere and a pyramid. Development of astronomy led to the emergence of trigonometry and spherical trigonometry.

Axiomatic Geometry

Euclid took a more abstract approach in his Elements, one of the most influential books ever written. Euclid introduced certain axioms or postulates expressing primary or self- evident properties of points, lines and planes proceeding rigorously to deduce other properties by mathematical reasoning. The thoroughness, which was one of the primary characteristics of Euclid’s approach, later came to be known as axiomatic or synthetic geometry.

Contemporary Geometry

Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which resembled approximately at small scales.

Euclidean Geometry

Euclidean geometry has become closely connected with computational geometry, computer graphics, convex geometry, discrete geometry and some areas of combinatorics.

Differential Geometry

The spaces that contemporary differential geometry considers are smooth manifolds whose geometric structure is governed by a Riemann metric and this attribute makes the study intrinsic. Differential geometry has been of increasing importance to mathematical physics due to Einstein’s general relativity postulation that the universe is curved.

Questions:

• What is Geometry?
• What is the difference between practical geometry and axiomatic geometry?