What are Geometric Tools? - Ruler, Compass, Protractor and Divider
We are surrounded by all kinds of shapes around us. Circular, spherical, triangular, cylindrical are just some of the various types of shapes that we encounter in our day-to-day life. Mathematics is a vast field of study which is branched into several other fields which often correlate to each other. The reason that we are surrounded by these shapes is that they are an integral part in many aspects which makes our lives easier. The study of these shapes of various sizes and dimensions is known as geometry. Geometry is one of the most widely studied branches of mathematics which has been igniting curiosity in human beings since ancient times.
The magnificent works of architecture that we see around us would not have been possible without the knowledge of geometry. Be it the Eiffel Tower in Paris or the beautiful Taj Mahal in India, all these astounding monuments are a miracle of geometry. Not only man-made works but the beauty of geometry could be found in mother nature herself!
Examples of Geometry Tools
Let us take a beehive as an example. A beehive is a perfect example of a hexagonal shape. Beehives are a constructional work made by bees and yet considering the perfectly smooth edges and the uniformity of the intricate structure we can say that geometry is something that can be done even by the simplest of beings. Consider the colorful rainbow.
A rainbow is an example of a perfect natural semi- circle. Even the beautiful seashells. In some of the seashells, we can see very intricate closely spaced patterns which are known as logarithmic patterns. And then how we neglect a spider web. In fact, a spider web is a shape. And then there’s the most common shape that we see and admire all throughout our lives. The spherical shape of a full moon. So, we can see that geometrical shapes not only exist in the boring studies of mathematics and science, but they also make up some of the most beautiful patterns and structures occurring naturally in nature.
Understanding the Technical Aspects of Geometry
Now let us get into the more technical terms of geometry. Broadly speaking, the types of geometry can be divided into three categories. One is the Euclidean geometry, the second is the elliptical geometry and the third is the hyperbolic geometry.
The first category of geometry, Euclidean geometry was the earliest type of geometry that was ever actually defined and explained. It was first studied by the Greek mathematician Euclid. Euclid formulated the basic five postulates in order to explain his geometry. After him, many other mathematicians carried on the study of geometry which provided us with the tremendous knowledge of one of the most important branches of mathematics.
Now when we talk about geometry the basic thought that comes in our mind is construction, that is the construction of various structures around us. As mentioned before, the construction of the colossal architectural works would have been impossible without the knowledge of the field of geometry. Now, the study of any field is not at all complete without the practical knowledge of the field.
The theoretical knowledge gives us an idea of how to do the work, but it would not actually help us to “do” that work. Here is where the importance of tools comes in. Various tools are required for various activities. As we require a shovel to dig the ground in the same way we will require various tools to create these geometrical shapes. Now, technically speaking, a tool is a means to bring about changes in one’s surroundings.
Use of Geometry Tools
With the help of tools, we can enhance our ability to do certain things and help us in accomplishing certain projects which would be otherwise, nearly impossible to achieve. To do a job we may need more than a single type of tool. In fact, more than often it is possible that that might require more than one type of tool. In order to draw the various types of geometrical shapes, we require various tools. To draw the shapes of the practical geometry we require tools like a ruler, a compass, a protractor, set squares, roller scales, and a divider, known as geometrical tools.
In the early days, the mathematicians who used to study the various geometrical shapes and sizes, used simple geometrical tools like a ruler and a compass. With more and more knowledge and the increasing need for new structural designs, a greater number of geometrical tools were incorporated in the field of geometry. Let us now look at some of the most commonly used geometrical tools:
A Ruler
A ruler is also called a straightedge. The name straightedge was more commonly used in the early days. Nowadays people use the word ruler. Now, a straightedge does what its name implies, that is, to draw straight edges. Thus, a ruler is used whenever we need to draw simple straight lines. The required length of the line is measured and then drawn. Now the measurement of the line can be in any form of the measurement unit.
The most commonly used measurement scales are the centimeter scale, the meter scale and the inches scale. Often the centimeter scale consists of a millimeter scale on one side and then the inches scale on the other side of the ruler.
A Compass
A compass is basically used to draw a circular figure. It can be used to draw a circle whose radius or the diameter is known, and it can also be used to draw an arc of some specified radius. Thus, if we need to draw a semicircle then also, we can use a compass. If we talk about the construction of a compass, then a compass usually has a metallic body and one of its ends is pointed. This is to give us the grip on the paper and define the center of the circle when we draw it. It is v in shape, and it comes with a pencil holder. The two arms of the compass can be adjusted based on the length required.
A Protractor
When we need to draw some angle then we use the geometrical tool known as a protractor. The protractor scale is graduated in degrees. Thus, it can also be used to measure any unknown angle. Generally, a protractor consists of the graduation scale from 0 degrees to 180 degrees. But it can also consist of a whole 360 degree of graduations, that is, a full circle.
A Divider
A divider almost looks like a compass. It is also v in shape. But unlike in a compass, it does not consist of a pencil holder in one of its arms. In a divider, both of its arms are pointed at one of their ends. When we need to compare two lengths of any measurement then we use the divider. It can also be used to measure the unknown length with the help of a ruler.
A Set Square
Now, if we need to draw a parallel line or even a perpendicular line then we can use a set square. To talk about the structure of a set square, it has a body which is usually made up of plastic. It is triangular and consists of graduations which can vary. There are usually two types of set squares. One is where the three angles of the triangle are 90 degrees and 45 and 45 degrees, whereas the other has angles as 90, 60 and 30 degrees.
Geometry Tools
Let’s get to learn more about geometry.
Meaning of Geometry
Imagine how tough it would have been for us to measure if Euclid couldn’t have created geometry, the basis for all our mathematical implementation related to size, shapes, figures and so on. To be precise, geometry is the measurement, it literally means “to measure earth” according to the Greek language system where Geo means ‘earth’ and Metron means ‘to measure’. It has been nearly 2000 years since geometry was created.
Geometry in Daily Life
The objects and figures we see around us as a television, bed, refrigerator, etc; couldn’t exist without geometry. While in primary school, students are introduced with geometry as shapes, their areas and volumes, and their construction but moving on to high school, they are made familiar to a broader aspect of identifying shapes and executing in daily lives, such as working on a building site as an architect also requires insightful knowledge about geometry. This shows that geometry plays a very important role even in the life of a student. Hence, it creates the root of mathematics for excelling in the subject.
Applications of Geometry in Daily Life
As an architect, geometry helps in mapping the building to be constructed.
It also plays an important role in the life of an artist as it guides them to design and express their ideologies in the best way possible, for example, while making a vase, it might help an artist to check the symmetry and proportionate size of the base on which the drawing is being made. Accessories and apparel are also designed by artists with the help of geometry only.
As a scientist, geometry acts as an instrument to track stars and planets and measure the distance between various elements of the solar system. This way, scientists can easily set the path for launching satellites
In the area of sports, such as football players, geometry helps them to aim the ball to score a perfect goal.
Nature is one of the easiest ways to learn geometry. Even kids are taken for a walk in the field to identify geometry with elements of nature such as leaves, flowers, clouds, stairs, et. Symmetry and shapes can initially be acquired by just discovering the surroundings.
Geometric Shapes in Daily Life
From a piece of paper to the planets, almost everything in this universe is the outcome of the execution of geometry. The shape of objects helps in differentiating among them as two-dimensional and three-dimensional figures. For example, a square is two-dimensional as it is a flat shape while a cube is three dimensional as it is a solid shape whose surface is nothing but a square. Two-dimensional shapes lie only on the x and y-axis whereas 3-D shapes lie in a plane that has x, y, and z axes.
Conclusion
Geometry has been playing a major role since ancient times, and having deep insight about tools can really help in the long term.
FAQs on Geometry Tools
1. How do geometry tools help us?
In the old times when modern machines and calculators did not exist, geometric figures could be drawn with the help of tools referred to as geometric tools. Initially, there were compasses and straightedges but with modernization, protectors, set squares and many other geometric tools have been introduced. One of the main areas where geometrical tools are often used is by an architect while designing the map of a building or a floor. These tools help in measuring lengths and identifying appropriate directions which make their work sorted.
2. Why is it important to study geometry?
The world couldn’t have been so advanced without geometry.
Example 1: The satellites launched by scientists are made and sent to the solar system with the help of geometry as it not only helps in the construction of spacecraft but also enables them to learn how these satellites have to be sent.
Example 2: In everyday life, while preparing food, we can weigh and measure quantities of ingredients only because geometry exists!
3. Who invented geometry?
Euclid invented geometry long back. He is often regarded as the father of geometry by the people. Since he is a great mathematician, he is known to have given some really important mathematical concepts that have become influential over time for us.
4. Who is the father of geometry?
Euclid of Alexandria is prominent as the father of geometry. Euclid’s invention of geometry remains one of the most essential parts of mathematics as it has enabled us to calculate and define geometry in the most explicit way possible. He defined mathematics in terms of proofs and didn’t believe anything without its geometric proof.
5. What are the different shapes in geometry? Give examples.
There are six main geometric shapes namely Circle, Square, Triangle, Rectangle, Parallelogram, and Trapezoid. Geometry shapes are further divided into 2-dimensional shapes such as circle, square, rectangle, etc and 3- dimensional shapes such as cube, cuboid, cylinder, etc