What Are Geometrical Designs Types Properties and Real World Examples
Before we get to know what geometrical designs are, we should first know what geometrical shapes are. Look closely around yourself, you will be able to see geometrical shapes infused in your surrounding objects. They are literally everywhere!
Geometrical Shapes
Many of the other geometrical shapes such as trapezium, parallelogram, cube, octagon, pentagon, ellipse, diamond, etc are made up with the help of these basic shapes which are squire, rectangle, triangle, and circle.
Basic Geometrical Shapes
What are Geometrical Designs?
Geometrical designs are designs formed by using basic shapes such as squares, triangles, rectangles, circles, etc to make patterns that look artistic and creative.
Geometrical Designs in a Square
If you look closely, then you will be able to see the geometrical design in a square made up of so many sizes of squares inside one. It indeed looks very eye-catching and beautiful, isn't it?
Geometrical Designs and Patterns in Indian Monuments
Did you know geometrical designs and geometrical patterns were used in Islamic art back in the olden days? In Islamic art, geometrical patterns were combined and arranged in such a way that they looked one of a kind and unique.
Geometrical art came into India during the Mughal period and it's quite obvious if we look at their buildings which were constructed in those times by very skilled laborers who had fine knowledge about patterns and how to carve designs on the walls, floors, pillars, windows, etc.
Taj Mahal and Qutub Minar have universally admired masterpieces of the world’s heritage and if you look at them, you will notice how beautifully the designs were made by using geometrical knowledge.
Geometrical Designs on Taj Mahal
Geometrical Designs on Qutub Minar
Things to Remember
Simple terminologies to remember before we learn how to design.
Circle: It is a polygon where all points on the circumference have an equal distance from the center.
Diameter: Any line which passes through the center of the circle which equally makes 2 halves of the circle.
Radius: Any line which connects the center and the circumference of the circle. Basically half of what diameter is.
Tangent: Only one point where the line just touches the circle from outside.
Chord: A line that does not pass through the center of the circle and connects two points on the circumference.
Triangle
Triangle is a polygon that has only 3 straight sides. The total sum of all the angles is always 1800.
Acute Angle: An acute angle is an angle that is smaller than 900.
Obtuse Angle: An obtuse angle is an angle that is bigger than 900
Right Angle: Angle which is exactly 900 and it can be denoted with the help of a squire marked inside.
Quadrilaterals
Any closed shape which has 4 straight sides.
Squire, rectangle, rhombus, parallelogram, and kite are a few examples of quadrilaterals. The total sum of the angles is always 360º.
How to Draw Geometrical Designs?
Well, drawing geometrical designs is not a big deal unless you have a creative mind and if you aren't creative, then there is no need to worry because we will be learning some of the easiest geometrical designs and patterns using geometrical shapes.
Following are some examples of easy geometrical designs.
Solved Examples:-
Example 1. Easy geometrical design using circles, diamonds, and squires
Complete Pattern in Example 1
Solution:
Solution of Pattern used in Example 1
Example 2. Easy geometrical design using rectangle and parallelogram
Complete Pattern in Example 2
Solution:
Solution of Pattern used in Example 2
Example 3. Easy geometrical design using triangles and ellipses.
Complete Pattern in Example 3
Solution:
Solution of Pattern Used in Example 3
Summary
Geometrical design is a very fun and creative way of mixing different shapes, lines, and curves together to create a unique and beautiful design. These designs are used in places such as in tattoos, interior designing of a house, wallpapers, jewelry, printing on clothes, etc.
Geometrical designs and shapes are majorly used by architects in order to draft detailed plans. Engineers strongly rely on geometrical principles to create or construct safely. For a fine drawing, geometrical knowledge is a must.
FAQs on Geometrical Designs and Their Creative Applications in Maths
1. What are geometrical designs in mathematics?
Geometrical designs are patterns or figures created using geometric shapes such as circles, triangles, squares, and polygons arranged according to mathematical rules. These designs are based on concepts like:
- Symmetry (line and rotational symmetry)
- Transformations (reflection, rotation, translation)
- Tessellations (repeating patterns without gaps)
- Proportion and ratio
Geometrical designs combine mathematical precision with artistic creativity and are commonly seen in architecture, art, and decorative patterns.
2. How do you create a simple geometrical design?
To create a simple geometrical design, start with a basic geometric shape and apply symmetry or repetition rules. Follow these steps:
- Draw a basic shape (e.g., a square or triangle).
- Use a compass or ruler to ensure accuracy.
- Apply reflection or rotation to repeat the shape.
- Arrange copies evenly to form a pattern.
For example, repeating a square in rows and columns creates a grid-based geometric pattern.
3. What is symmetry in geometrical designs?
Symmetry in geometrical designs means that a figure remains unchanged after a specific transformation like reflection or rotation. The main types are:
- Line symmetry: The figure can be folded into two equal halves.
- Rotational symmetry: The figure looks the same after rotation by a certain angle.
For example, a square has 4 lines of symmetry and rotational symmetry of order 4.
4. What is a tessellation in geometric patterns?
A tessellation is a repeating pattern of shapes that covers a plane without gaps or overlaps. Only certain shapes tessellate perfectly, such as:
- Equilateral triangles
- Squares
- Regular hexagons
For example, regular hexagons fit together because each interior angle is 120°, and three angles meet to form 360°.
5. What is the formula for the interior angle of a regular polygon?
The formula for the interior angle of a regular polygon is [(n − 2) × 180°] / n, where n is the number of sides. For example:
- For a regular hexagon (n = 6):
[(6 − 2) × 180°] / 6 = 120°
This formula helps in constructing accurate geometric designs and tessellations.
6. What is rotational symmetry in geometric designs?
Rotational symmetry occurs when a figure looks the same after being rotated by a certain angle less than 360°. The order of rotational symmetry is calculated as:
Order = 360° / smallest angle of rotation
- A square rotates every 90°.
- Order = 360° / 90° = 4.
This concept is widely used in mandala art and circular geometric patterns.
7. How are transformations used in geometrical designs?
Transformations such as reflection, rotation, translation, and dilation are used to create repeating and symmetrical geometric patterns. These include:
- Reflection: Flipping a shape over a line.
- Rotation: Turning a shape around a point.
- Translation: Sliding a shape without changing its size.
- Dilation: Resizing a shape proportionally.
By combining these transformations, complex and creative geometrical designs can be formed.
8. What is the difference between geometric shapes and geometric patterns?
A geometric shape is a single figure like a triangle or circle, while a geometric pattern is a repeated arrangement of shapes following a rule. For example:
- A triangle is a geometric shape.
- Repeating triangles in a symmetrical arrangement forms a geometric pattern.
Patterns involve repetition, symmetry, and mathematical structure, while shapes are the basic building blocks.
9. Where are geometrical designs used in real life?
Geometrical designs are used in architecture, art, textiles, and engineering to create visually appealing and structurally balanced patterns. Common examples include:
- Mosaic tiles and floor tessellations
- Islamic geometric art
- Mandala patterns
- Building structures based on polygons and symmetry
These applications show how mathematics and creativity work together in real-world designs.
10. What are common mistakes to avoid when making geometrical designs?
Common mistakes in geometrical designs include inaccurate measurements and ignoring symmetry or angle rules. To avoid errors:
- Use a ruler and compass for precise construction.
- Check angle measures using correct formulas.
- Ensure repeated shapes align without gaps in tessellations.
- Maintain consistent proportions.
Accuracy in measurements and transformations ensures the design remains mathematically correct and visually balanced.
