Geometry is all about shapes and the properties of shapes. If your child likes playing with objects, or like drawing, then geometry is for him/ her. The student is familiar with the physical objects about him, such as a ball or a block of wood. By a careful study of the following exercise, he may be led to see the relation of such physical solids to the geometric figures with which he must become familiar.
Geometry can be divided into:
- Plane Geometry
- Solid Geometry
Plane Geometry is about flat shapes like lines, triangles, squares and circles. These shapes can be drawn on a paper. Where the angles at the base of an isoceles triangle are equal.
Point, Line, Plane and Solid
- A Point has no dimensions, only position
- A Line is one-dimensional
- A Plane is two dimensional (2D)
- A Solid is three-dimensional (3D)
Solid Geometry is about three dimensional objects like cubes, spheres, prisms and cylinders. They are rectangular boxes of various shapes such as, cones, spheres, and lines in three space.
Why do you think Geometry is Important?
Take for example a block of brick or a box and observe it closely. Have you ever wondered?
- Has it weight?
- Has it color ?
- Has it taste ?
- Has it shape ?
- Has it size ?
These are called properties of the solid. And this solid is called as a physical solid. So let’s think about
- Properties of this solid apart from the block of brick ? Imagine the brick is removed.
- Can you visualize the space that it occupied?
- What name would you give to this space?
- What properties did the brick possess?
- What is its shape and size?
- What is it that divides this geometric solid from adjacent the space?
- How thick is this surface and how many surfaces has the brick?
- Where do they intersect and how many intersections are there? How wide how long?
- How wide and how long are the intersections?
- We can go on and on questioning an entity at a solid state.
Geometry gives us answers to all the questions above for any shapes.We study Geometry to discover patterns, find areas, lengths, volumes and angles, and perceive better the world around us.
The important concepts of Geometry are:
- The space, in which we live, though endless and infinite in amount, may be believed as divided into parts. A physical solid uses a limited share of space. The share of space occupied by a physical solid is called a geometric solid.
- A geometric solid has length, breadth, and thickness. A geometric solid may be divided into parts. The margin of a solid is called a surface.
- A surface is not a part of a solid. It has length and breadth, but no thickness. It may be divided into parts. When a line moves in space, the path it moves will be known as the surface. The margin of a surface is called a line.
- A line is not a part of a surface; it has only length and may be divided into parts. The path in which a point moves is known as a line. The margin or extremity of a line is called a point.
- A point is not a part of a line. A point is a dot with a pencil on a piece of paper and is known as the geometrical point. It has neither length, nor breadth, nor thickness. It cannot be divided into parts but a position only.
Definitions of the four fundamental concepts :
- A geometric solid is a defined share of space.
- A surface is that which defines a solid or separates it from an adjoining solid or from the surrounding space.
- A line is that which has length only.
- A point is position only.
A geometric figure can be a point, a line, a surface, or a solid, or a combination of any or all of these. Two geometric figures are said to correspond if, when either is placed upon the other, each point of one lies upon some point of the other. A line is generally labeled by two capital letters, as line AB. If two lines meet, but are not vertical to each other, they are said to be oblique. The study of geometry ensues from a small number of accepted truths such as axioms or postulates, and then forms true statements using a methodical and difficult step-by-step proof. However, there is much more to geometry than the relatively textbook approach, as evidenced by unforeseen results of projective geometry.
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