NATIONAL MATHEMATICSYEAR

MATH'S EXHIBITION2012

Visualising solid

shapes

Introduction

You have already learnt about plane shapes and solid shapes. Plane shapes are those shapes which have only two measurements like length and breadth and therefore they are called 2-Dimensional or 2-D shapes whereas solid shapes are those shapes which have three measurements like length, breadth and height or depth. Hence, they are called 2-Dimensional or2-D shapes. As you know that triangle, square, circle, rectangle etc,.. Are known as 2-D figures while cuboids, cube , cylinder, cone, sphere etc.., are known as 3-D figures.

2-D3-D2-D 3-D

Figure of the shape Type of shape Name of the shape

2- dimensional Square

2-dimensional Triangle

3-dimensional Cube

2-dimensional Rectangle

2-dimensional Circle

3-dimensional Cuboid

3-dimensional Cylinder

I n o u r p ra c ti c a l l i fe , m a ny a ti m e s w e c o m e a c r o s s c o m b i n a ti o n o f d i ff e r e n t s h a p e s . Fo r

exa m p l e , l o o k a t t h e fo l l o w i n g o b j e c t s .

A photo frameA rectangular

path

A bowlA hemispherical

shell

A batteryA cylindrical

shell

TOP VIEW

SIDE VIEW

FRONT VIEW

Top view

Front view

Side view

You have studied that a 3- dimensional object look differently from different position so they have been drawn from different perspectives. For example, a given car have the following views..

Map • A map is a representation of a geographic area,

usually a portion of the earth’s surface. It may be shown in many different ways, from a traditional map printed on paper to a digital map built pixel by pixel on the screen of a computer. Maps can show almost anything, from the electric supply grid of your community to the terrain of the Himalayas to the depths of the ocean floor. A map can be practical, directing travelers from one point to another through confusing terrain, or explaining the world by attaching specific types of information to geography. But maps can also entertain and invite exploration.

information to geography. But maps can also entertain and invite

For example, a colorful map of the Marquesas Islands with exotic-sounding ports such as Hakapehi on Nuku Hiva might have a beckoning appeal to some. Similarly, a detailed map of the many features of Athens or Bangkok might entice others to travel to these sites. A map can even be created for the surface of Mars, based on data transmitted to Earth from computer-controlled spacecraft, showing places that most people will never visit.

The first question to ask about a map is what its theme is. The theme is the particular aspect of the world that the map attempts to show, such as roads, borders, vegetation, or statistical data. Maps can be divided by theme into three categories. The first, general maps, are those that contain many themes and give a broad picture. General maps are often practical, showing the world in a way that allows people to get from one point to another without getting lost, or allows them to learn about the overall layout of an unfamiliar place without having to go there.

An example of a general map is a road map of a country showing major cities, mountains, rivers, landmarks, etc. The second category is thematic maps, which contain one or a few themes and show in-depth informatatic maps can show almost any kind of information that varies from place to place, such as a country’s population or income level by state, province, or county, with each division colored differently to indicate the relative level of population orincome.

.

The third category of map is charts, which are accurate maps of routes of travel used for ocean and air navigation. They must be updated frequently so that captains and pilots know of current dangers along their route.

library court college

cemetery bus stopschoolpark

Main street

Road

Road map of a city

Post office

AJC

Bose

road

Denim street

Police station shop

Foot

pat

h

PolyhedronsPolyhedron, in geometry, a solid bounded by flat surfaces with each surface bounded by straight sides. In other words, a polyhedron is a solid bounded by polygons. Each of the flat surfaces is called a face. A straight side bounding a face is called an edge. A point at the end of an edge is called a vertex. Figure 1, a pyramid with a square base and four triangular sides, is an example of a polyhedron.

In a regular polyhedron all of the faces are regular polygons that are congruent (equal in size and shape). The only regular polyhedral are the five shown in figure 2. They are the tetrahedron, which has four triangular faces; the cube, which has six square faces; the octahedron, which has eight triangular faces; the dodecahedron, whose 12 faces are all regular pentagons; and the icosahedron, which has 20 triangular faces. These are sometimes referred to as the Platonic solids because they appear in the writing of the Greek philosopher Plato, representing fire, air, earth, water, and the universe as a whole.

A convex polyhedron is one in which a line segment connecting any two vertices of the polyhedron contains only points that are on a face or inside the polyhedron. For convex polyhedrons, the relationship between the number of vertices v, faces f and edges e is given by v + f - e = 2. For example, the cube has 8 vertices, 6 faces, and 12 edges, which gives 8 + 6 - 12 = 2. The value of v + f - e for a general polyhedron is called the Euler characteristic of the surface of the polyhedron, named after the Swiss mathematician Leonhard Euler. It can be calculated for general polyhedral using the methods of algebraic topology, a branch of mathematics.

Vertex

Face

Edge

Lateral surface

Base

Edges, Faces, and Vertices

Made by:- Priya Mishra

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