Formula Sheet: Symmetry

A line of symmetry divides a figure into two mirror-image halves. This concept is used in art, nature, and design to create balanced and harmonious structures.

The angle of rotation for a figure with n identical segments to match its original position. This applies to objects like wheels and stars, ensuring uniform appearance upon rotation.

For a figure with n angles of symmetry. Each angle can be calculated using this relation, useful in understanding regular polygons and their properties.

Figures such as squares and circles exhibit symmetry. The identification of symmetrical properties aids in designing aesthetically pleasing shapes.

A square has lines of symmetry along its vertical, horizontal, and both diagonal axes, making it a perfect example of symmetry in two dimensions.

Defines that a rectangle can be divided into two identical parts along its vertical and horizontal midlines, useful in architectural designs.

An equilateral triangle has three lines of symmetry. This can be demonstrated through folding, highlighting the balance in triangular designs.

A circle can be divided into symmetric sections from any diameter, demonstrating perfect rotational and reflectional symmetry.

A regular polygon has the same number of lines of symmetry as it has sides (n), showcasing uniformity in geometric shapes.

Symmetry in nature, such as flowers and animals, follows mathematical principles to create visually appealing patterns.

A figure with 4 angles of symmetry will look the same when rotated by 90°, 180°, 270°, and 360°, useful in identifying symmetrical properties of shapes.

φ is the angle of incidence, demonstrating the relationship of angles when light is reflected on a symmetrical surface.

If a figure can be divided into two identical parts, it can be represented mathematically as having a line of symmetry.

Symmetrical properties involve transformations like reflection or rotation while maintaining the original figure, crucial in design and construction.

This formula helps derive the interior angles of polygons, linking symmetry to geometry.

Defines periodic symmetry where n stands for number of identical sections in a figure, applicable in various geometric contexts.

Where n refers to the number of equivalent sections when a shape is folded symmetrically, illustrating balance.

Here, k indicates the number of segments reflecting across a center line; this highlights design principles in aesthetics.

Each section's area can be determined, combining symmetric principles in practical applications like tile patterns or fabric designs.

R is the reflective edge ratio of a symmetric shape to its base area, linking geometrical and artistic perspectives.