Geometry

Geometry, a word derived from Ancient Greece meaning Geo= Earth, Metron= Measurement. So how does one define geometry in simple words, Math geometry is one of the major branches of mathematics, it is defined as a branch which deals with the understanding and application of shapes and sizes. So In this article we will learn more about geometry.
 

1. Euclidean Geometry: Euclidean geometry looks at the study of solids and planes. It introduced two major types of shapes, 2 Dimensional (2D) 3 Dimensional (3D). Flat shapes such as square, triangle, circle etc… are known as 2D shapes. Whereas Solid shapes such as cube, cuboid etc… are known as 3D shapes. These are some basic geometry shapes to remember.

2. Non-Euclidean Geometry: There are two types of Non-Euclidean Geometry, namely spherical and hyperbolic geometry. Spherical Geometry talks about the study of plane geometry on a sphere. On the other hand, Hyperbolic geometry deals with the study of 

3. Convex Geometry: This branch of mathematics deals with study of convex sets and its properties and has various applications of optimization and functional analysis.

4. Topology: It's the study of shapes that can be stretched and also be moved while the points on the shape continue to stay close and together with each other.
 

There are few fundamental formulas when it comes to understanding geometry. They can be divided into 5 main categories

1. Area Formulas: These are the geometric formulas used to calculate and measure plane figures, a few of the important formulas include.

Rectangle: A= L×W

Square: A= S²

Triangle: A= πr²

Circle: A= π×r²

^{2. Perimeter or Circumference Formulas:} These formulas help us to calculate the length of the boundary of a shape. Below are some basic formulas to find the perimeter of shapes.

Rectangle: 2×(length+width)

Square: 4×side

Triangle: side1​+side2​+side3​

Circle: 2×π×radius

3. Volume formula: Volume formula is normally used to find out the amount of space inside a given 3D shape. Some basic formulas are given below.

Cube: V= side³

Rectangular Prism: V= length×width×height

Sphere: V= 4​/3×π×radius³

Cylinder: V= π×radius2×height

4. Pythagorean Theorem^: Pythagoras theorem states that the square of the length of the hypotenuse of a triangle is equal to the sum of the squares of the length of the remaining two sides. The Pythagoras formula is expressed as a²+b²=c².

5. Trigonometric ratios: Trigonometric ratios help in relating the angles and sides of a right-handed triangle. Some of the most important trigonometric ratios are

sin(θ)=hypotenuse/opposite​

cos(θ)=hypotenuse/adjacent​

tan(θ)=adjacent/opposite​

1. Remembering the formulas: It is always important to know all the basic formulas in geometry while solving any sum. This will give you a very good advantage.

2. Drawing the Diagrams: Students should always practice drawing the diagram first, which will help them understand the concept much better.

3. Always label everything: Labelling each side and angles of a diagram will help you to not miss out or make major mistakes while solving problems. 

4. Take advantage of special geometry tools: Using tools such as compass, protractor, divider etc… will help you in reaching the results quicker. 

5. Learn to use graph paper: Graph paper is another key element in geometry which will help you in plotting points and calculating units easily

The concept of geometry is very important and interesting to learn and apply. Geometry has helped us evolve and invent new things throughout centuries on the hindsight without geometry we may have not hand simple mode of transportation. This indicates us to how important it is to understand geometry in our current society. Though we may be moving towards Ai and robotics in the future, but a strong understanding of geometry is needed to achieve these future dreams and ideas.