Chapter 4

Geometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Have you ever pondered that the various shapes and objects we see in our daily lives are a part of geometry? Indeed, geometry is the branch of mathematics that comprises shapes, angles, dimensions, and sizes of different objects and even represents 3D and 2D figures. Basic geometry is based on points, lines, and planes. To calculate the area, perimeter, and volume of shapes, geometric concepts are widely used. For example, a circle also refers to a geometrical shape made with the help of a curve that always has the same distance.

There are five branches of geometry, namely:

  • Algebraic geometry: This is one of the branches of geometry that deals with the multivariate, polynomial zeros. Algebraic geometry is based on abstract algebraic methodologies required to solve geometric problems related to zeros. It is applied in phylogenetics, cryptography, string theory, etc. Today, algebraic geometry holds a focal role in modern mathematics. 
  • Discrete geometry: This is also known as combinatorial geometry. It refers to studying geometrical objects like points, lines, triangles, and circles that are discrete either by their nature or by their exhibition. This topic mainly covers the combinatorial properties of various objects and assists in establishing relationships among them.
  • Differential geometry: Differential geometry is a mathematical discipline that employs differential calculus, integral calculus, linear algebra, and multilinear algebra to investigate quandaries in geometry. It was found by Sir Isaac Newton and Leibniz for plane bends in the 17th century and by the Swiss mathematician Leonhard Euler for bends in space in the18th century.
  • Euclidean geometry is a prominent branch of mathematics, coined by Alexandrian Greek mathematician Euclid in his book on geometry. Euclid’s technique comprises accepting a little arrangement of instinctively engaging and reasoning numerous recommendations from these. In other words, it represents the axiomatic system where true statements are derived from small axioms. 
  • Convex geometry: In mathematics, convex geometry refers to convex sets in the spheres of computational geometry, convex analysis, discrete geometry, probability theory, game theory, etc.
  • Topology: It pertains to the properties of a geometric object that demand continuous mapping. It has various applications in proximal continuity, proximity spaces, separation axioms, and uniform spaces.

There are four types of angles in geometry: 

  • Acute angle – An acute angle is an angle that falls between 0 and 90 degrees.
  • Obtuse angle – An obtuse angle is more than 90 degrees but less than 180 degrees.
  • Right angle – An angle of 90 degrees is known as a right angle.
  • Straight angle – A straight angle is 180 degrees, determined by a straight line.

A quadrilateral refers to a four-sided 2D figure, the sum of whose internal angles is 360°. The name quadrilateral is derived from two Latin words, ‘quadri’ and ‘latus,’ meaning four and side, respectively. It becomes pivotal to distinguish the properties of quadrilaterals to establish their differences from polygons. It can also be used in the construction of quadrilaterals. There are two basic properties of quadrilaterals:

  • A quadrilateral always has four sides.
  • The sum of all four internal angles of a quadrilateral is always 360°.

There are five types of quadrilaterals:

  • Parallelogram
  • Rectangle
  • Square
  • Rhombus
  • Trapezium

A shape is termed symmetrical when it is the same on both sides where lines can be drawn to show both sides are equal; whereas, a shape has symmetry when a mirror line can get drawn on it that reflects both sides are same or equal.

In a nutshell, geometry helps calculate the area, perimeter, volume, and various measures using the length, breadth, and height of different geometrical figures. There are a plethora of ways used in geometry in solving numerous complex problems. Geometry is easy to learn, and with practice, one can easily excel.

  1. What are the basic elements of geometry?
    There are three basic elements of geometry:

    • Point
    • Line
    • Plane
  2. What does geometry mean?
    In layman language, geometry refers to the measurement of Earth. The word ‘Geometry’ has been derived from the two Greek words—‘geo’ meaning Earth and ‘metron’ meaning measurement. Anything that you see around has its shape, which is called geometry.
  3. What are some applications of geometry?
    Having practical knowledge of geometry can help in various ways. Some of the applications of geometry include:

      • Measurement of a line and surface area of land.
      • To measure the dimensions of the land.
  4. Is geometry easier than algebra?
    Geometry is easier to understand and comprehend as compared to algebra. When it comes to algebra, it is more related to the complex equation, and Geometry is focused on finding the length of shapes and the measure of angles. Geometry is easy to apprehend and fun to learn.

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