Have you ever tried to find out the difference between the shape of a credit card and a box? Or a thin crust pizza and a football? Well, the major difference between the aforementioned pair is the width. Objects like thin-crust pizza and credit cards are flat whereas objects like a box or a football are not.
Two-dimensional shapes are the flat plane figures that can be represented on a piece of paper or flat surface. These shapes have length and breadth but no considerable width or thickness. Shapes like circles do not have length and breadth but it can be defined by a radius which is actually the distance between its centre and boundary. Even circles do not have a thickness to be defined like all the other 2d figures. Examples of 2d shapes are plates, cards, sheets, clocks, windows, etc found in our day to day life.
All the shapes found on Earth are basically of two types - 2D and 3D. 2D stands for 2 dimensional and 3D stands for 3 dimensional. Dimension is a spatial space where the position of every point of an object can be specified with the help of a minimum number of coordinates. A line can be defined in one-dimension because the position of all the points on a line can be described by only one coordinate. Flat objects that can be represented on a plane are two-dimensional objects as it requires two coordinates to specify the position of the points in the object. Three-dimensional objects are the objects having points whose position can be specified by using three coordinates.
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Mathematicians and scientists like Euclid and Pythagoras started developing theorems on areas, angles and perimeters of two-dimensional shapes. Later, the cartesian coordinate system was made to specify pairs of numerical points on a plane. In 1637, Descarte wrote about the idea of the system having two perpendicular axes. Pierre de Fermat also worked on the same but in 1649, Frans van Schooten brought in the concept of using a pair of axes.
All two-dimensional shapes can be represented in the Coordinate system. Coordinate systems are defined by the number of lines. A number line has zero marked in the middle and numbers starting from one on either side of zero that goes to infinity. The difference between both sides is the sign as one side contains positive numbers and the other side contains negative numbers.
In the cartesian coordinate system for the plane, there are two perpendicular number lines (x-axis and y-axis) such that the middle of both the number lines intersects with each other to have a common zero. The position of any point on a plane can be defined by a pair of two numbers, where one number coordinates with the x-axis and the other number coordinate with the y-axis. Thus, the pair of numbers defining a point is called coordinates of a point.
As discussed, two-dimensional shapes can be represented on a coordinate system and each point on the shape correlates with x and y-axis. The 2D shapes names given below are two-dimensional figures having edges, vertices and angles. It can be divided into two broad sections and then into further divisions:
A circle is a simple two-dimensional closed curve 2D drawn in such a way that each point on the circle is at equidistant from the centre. This fixed distance is called a radius (R). The line passing through the centre touching the two opposite points on the surface is called diameter (D) which is double the radius. Around the centre of the circle ‘O’ it is 360 degrees.
Ellipse is a 2D plane shape more like an oval that is a circular shape bulged at two sides. Unlike radius, an ellipse does not have a radius or any fixed distance of the points on the surface from the centre of the ellipse. There are two perpendicular axes - minor axis (passing through the flattened side) and major axis (passing through the bulged sides). It has two focal points on the axis passing through the bulged sides.
Polygons are the plane closed figures having more than two sides. The basic figures of polygons are - Triangles (having 3 sides), Quadrilaterals (having 4 sides), Pentagons (having 5 sides), Hexagon (having 6 sides), Heptagons (having 7 sides), Octagons (having 8 sides), etc. Except for circles, eclipse and other similar shapes, almost all the other 2D shapes are considered as polygons. Polygon is a part of elementary geometry that contains a finite number of line segments connected to each other edge to edge to form a closed figure. It has sides, edges, corners, angles and vertices.
A triangle is a polygon with three sides. It is a two-dimensional shape having a flat surface which can be drawn on a piece of paper. A triangle consists of three sides, three vertices and three angles. In other words, we can say that a Triangle is the simplest polygon. The most basic fact about the triangle is that the sum of all the interior angles of a triangle is always 180 degrees.
Triangle can be classified into three types on the basis of sides:
Scalene Triangle - all three sides are of different lengths
Isosceles Triangle - any two sides are of two-lengths
Equilateral Triangle - all the three sides are of the same length.
Triangles can be classified into three types on the basis of sides:
Acute triangle - all the angles are less than 90 degrees.
Obtuse triangle - one angle out of all three angles is more than 90 degrees.
Right triangle - one angle out of all three angles is exactly 90 degrees.
According to the plane geometry, a quadrilateral is a four-sided polygon having four vertices and four angles. There are different types of quadrilateral - square, rectangle, parallelogram, trapezoid, rhombus and kite. Here, we will discuss the two basic shapes, that is square and rectangle.
A square is a four-sided polygon having four equal sides and angles. The opposite sides are also parallel to each other and the angle between two adjacent (near) sides are always 90 degrees. The distance between two alternate angles called diagonals bisects each other at 90°.
A rectangle is also a four-sided polygon but the length of all the four sides are not same. The two opposite sides of a rectangle are of the same length. Just like a square, all the angles of a rectangle are at 90°.
Pentagon is a polygon of five sides. The length of the sides of a pentagon may or may not be the same. Pentagons with equal sides are called regular pentagons whereas the ones with unequal sides are called irregular pentagons. The interior angle of a regular pentagon is 108 degrees.
Hexagon has six sides, six angles and six vertices. There are two types of hexagon - regular and irregular. It is a two-dimensional shape and is represented by two coordinates namely x-axis and y-axis. In case of a regular hexagon, each angle is 120 degrees.
Heptagon is a seven-sided polygon having seven angles and seven vertices. A regular heptagon has interior angles of 12847 degrees each.
A polygon having eight sides is called an octagon. It is a two-dimensional shape having eight vertices and eight angles such that a regular octagon has each angle of 135 degrees.
1. Why is it not possible for a polygon to have one or two sides?
According to the definition, a polygon is a closed figure formed by straight lines having a particular angle between them. Now, it is a matter of fact that no closed figure can be drawn from just two lines. Even if we manage to connect both the lines end to end with each other, the angle between the lines will become zero and thus the resulting figure will be a straight line.
2. Why is a circle not a polygon?
Polygon is a closed figure made up of finite set straight lines connected end to end whereas a circle is a closed curve and not made up of straight lines.