SIMETRIA

Introduction

In this tutorial, we will explore the concept of symmetry, including different types such as axial symmetry, rotational symmetry, and translational symmetry. We will also examine symmetry in nature, letters, and geometric shapes. This guide is designed to help you understand and identify various forms of symmetry, making it a valuable resource for students and anyone interested in mathematics.

Step 1: Understanding Symmetry

• Definition: Symmetry is a relationship of parity concerning the height, width, and length of the parts that make up a whole.
• Types of Symmetry:
  • Axial or Reflective Symmetry
  • Rotational Symmetry
  • Translational Symmetry
  • Bilateral Symmetry
  • Radial Symmetry

Step 2: Exploring Axial Symmetry

• What is Axial Symmetry: It occurs when one half of a figure is a mirror image of the other half.
• Identifying Axial Symmetry:
  • Draw a line (axis of symmetry) through the figure.
  • Ensure that the parts on either side of the line are identical.

Step 3: Symmetry on the Number Line

• How to Illustrate: Plot points on a number line and identify symmetrical points relative to a central point.
• Example: If 3 is on one side of 0, then -3 is on the opposite side.

Step 4: Symmetry in Letters

• Identifying Symmetrical Letters:
  • Some letters like A, H, I, M, O, T, U, V, W, X, and Y are symmetrical.
• Practical Tip: Write each letter and draw lines to check for symmetry.

Step 5: Symmetry in Geometric Shapes

• Types of Shapes: Analyze squares, circles, triangles, and rectangles.
• How to Identify:
  • Determine the axes of symmetry for each shape.
  • Count the number of symmetrical lines.

Step 6: Rorschach Inkblot Symmetry

• Concept: This involves visual reflections where one side mirrors the other.
• Activity: Create your own inkblot and fold it to see the symmetry.

Step 7: Understanding Rotational Symmetry

• Definition: A shape has rotational symmetry if it can be rotated (less than a full circle) about a central point and still look the same.
• Identifying Rotational Symmetry:
  • Find the center of the shape.
  • Rotate and see how many times it looks the same within 360 degrees.

Step 8: Calculating the Angle of Rotation

• Formula: Angle of rotation = 360° / Number of identical positions.
• Example: A shape with 4 identical positions has an angle of 90°.

Step 9: Creating a Windmill (Catavento)

• Materials Needed: Paper, scissors, a pencil with an eraser, and a pushpin.
• Steps:
  • Cut a square piece of paper.
  • Mark the center and cut diagonally towards the center but not all the way through.
  • Fold alternate corners towards the center and secure with a pushpin.

Step 10: Exploring Translational Symmetry

• Definition: A figure has translational symmetry if it can be moved (translated) along a certain direction and still appear the same.
• Real-World Example: Wallpaper patterns.

Conclusion

Understanding symmetry enhances your appreciation of mathematics and its applications in the world around you. By exploring different types of symmetry through practical examples and activities, you can deepen your knowledge and skills. Consider practicing these concepts with real-world objects or drawings to reinforce your learning. Happy studying!