Dimension means the measurement of the size or distance of an object or space in just one direction. It is believed that the Universe has 10 dimensions, but fortunately, the human eye can only comprehend three.
In general, there are four types of dimensions: Zero dimension, One dimension, Two-dimension, and Three-dimension. In this lesson, we will learn about the different types of dimensions and also know the facts about fractional dimensions.
|1.||What is Dimension?|
|2.||Formula of Dimension|
|3.||Facts of Dimension|
|4.||How Many Dimensions Are There?|
|5.||Dimensions of Units|
What is Dimension?
Dimension is a measure of the length, width, or height extended in a particular direction. The letter D in 2D, 3D represents dimensions. Now, let us look at some examples of different dimensions given below.
- Zero dimension: A point has no extent in any direction, so it has no dimension.
- One dimension: A line consists of only one dimension, which is its length.
- Two-dimension: A piece of paper has two dimensions, length and width.
- Three-dimension: Dices have three dimensions, length, width, and height.
Formula of Dimension
Dimension is a measure of a point or line extended in one direction and we know that every shape around us has some dimensions. The concept of dimension does not have any specific dimension formula. The value and the number of dimensions vary, based on their shape and size. The following table illustrates the dimension formulas of polygons and circles.
|Number of Dimensions||Physical Quantity||Dimension Formula||Dimensions Used|
|2D - Polygons||Area||length × width (or) height||length, width (or) height|
|Perimeter||Adding all the distance around the shape||distance|
|2D - Circle||Area||π r2 (or) π d||radius (or) diameter|
|Circumference||2 π r||radius|
Dimensions can be used to find the unknown values of objects with the help of formulas. For example, if the perimeter of a square is 8 inches, we can find its length by using the dimension formula: Perimeter = 4 × Length. Substituting the value of perimeter in the formula, we get: 8 = 4 × Length. Therefore, Length = 2 inches.
Facts of Dimension
The meaning of dimension plays a different role in different areas. Its meaning differs in mathematics and physics. The concept of dimension in math is the point or value, measuring the object. Have you heard about fractional dimension? Well, before that we will have a short note on fractal geometry.
Fractal geometry helps in sorting out these questions where it is entirely connected with nature. Traditional geometry defines the shape using some formulae, whereas fractal geometry uses multiple iterations. The dimensions used in fractal geometry are called fractal or fractional dimensions. Look at the example explained below. Consider a square that is broken into many pieces and has formed a square grid. Here, the traditional dimensions do not work. However, the fractional dimension helps in measuring an object which is broken or formed with many pieces.
The formula to calculate the fractional dimension is given by log(number of self-simulation process) / log(magnification factor). Here, the magnification factor is the degree of enlargement of an object.
How Many Dimensions Are There?
We know that there are three dimensions existing in space. A point has zero dimension, a line has one dimension (x-axis), a plane has two dimensions (x, y-axis) and a solid figure has three dimensions (x, y, z-axis). So, in general, there are four types of dimensions as given below.
- Zero Dimension
- One Dimension
- Two Dimension
- Three Dimension
Observe the examples of dimensions shown below.
The meaning of dimension in physics represents mass, time, and length. Many of us have a question about the existence of the fourth dimension. Yes! It's time. Time is represented in the fourth dimension. We can see only three dimensions across the globe. However, many scientists are researching to find out the existence of the ten dimensions.
Dimensions of Units
Different units are used to measure different quantities like length, temperature, area etc. The following table shows the dimensions that are usually used for units like length, area, temperature, volume and weight.
|Length||inch (in), feet (ft), yards (yd), miles|
|Temperature||Kelvin (K), Fahrenheit (F), Celsius (C)|
|Area||Square Inch, Square Feet, Acre, Square Yard, Square Mile|
|Volume (Capacity)||Fluid Ounces (fl oz), pint (pt), quarts (qt), gallons (gal)|
|Weight (Mass)||Ounces, Pounds (lb), Tons|
Sam wants to find out the area of a soccer field. What are the dimensions needed to find out its area?
A soccer field's area can be measured if we know its length and width. So, length and width are the two dimensions required.
Anna plans to make a wooden wardrobe in her living room. What are the dimensions needed to make a wardrobe?
The wardrobe can be made only if Anna knows its length, width, and height. So, length, width, and height are the needed dimensions.
George wants to pack all his old books in a box. What should he know about the box? What are the dimensions that must be verified?
He must know the length, width, and depth of the box. He must also verify if the box can occupy all the books, i.e., the volume of the box. So, the length, width, and depth must be verified to know its volume.
FAQs on Dimension
What do 5 Dimensions Look Like?
The fifth-dimension is invisible to the human eye as it denotes a tiny circle in space. Some scientists are researching the existence of ten dimensions.
What is the Use of Dimensional Formula?
A dimensional formula is used to calculate the area, volume, perimeter, etc. of any object.
What are 3 dimensional and 2-dimensional shapes?
2-dimensional shapes are shapes with only two dimensions. For example, shapes like rectangles and squares are 2-dimensional shapes. 3-dimensional shapes are shapes which have three dimensions. For example, cubes and cones are 3-dimensional shapes.
What is the Meaning of Dimensional Analysis?
Dimensional analysis means to find the physical quantities and analyze the relationship between them. It helps us to study the nature of distinct objects like the flatness and straightness mathematically.
What are Dimensionless Quantities?
The quantities which have no dimension are called dimensionless quantities. Such quantities have a fixed value. For example, the constant Pi - π is a dimensionless quantity because it has a fixed value.
What are Dimensional Variables?
Dimensional variables are those quantities which have dimensions with changing numerical value, or which do not have a fixed value. For example, force, work done, energy, speed.
Why do we Change Dimensions?
Conversions of dimensions are important to solve many real-time problems, be it the exchange of money, purchasing and selling, cooking, baking, etc.