Glossary

Associativity
Axis of symmetry
Center of rotation
Circle
Congruence
Congruent angles
Dilation
DNA
Equilateral triangle
Function
Graphs of functions
Glide reflections
Group
Laws of nature
Line
Order of symmetry
Palindrome
Polygon
Vertex of a polygon
Reflection
Reflectional symmetry
Rigid transformation
Rotation
Rotational symmetry
Scale factor
Similar
Square
Symmetry
Symmetry group
Transformation
Image of a transformation
Translation
Translational symmetry
AA condition for triangles

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Transformations and SymmetryIntroduction

Reading time: ~5 min

Many geometric concepts like lines

or polygons were “invented” by mathematicians. Symmetry, on the other hand, is everywhere around us. Almost all plants, animals, and even we humans are symmetric.

Butterfly
Lion
Starfish

Over time, we’ve imitated nature’s symmetry in art, architecture, technology and design. Symmetric shapes and patterns just seems to look more beautiful than non-symmetric ones.

Taj Mahal
© Yann Forget / Wikimedia Commons
US Capitol
© Martin Falbisoner
Mosaic Church Window

But symmetry is much more important than simply looking beautiful. It lies at the very foundations of our universe, and can even explain the most fundamental laws of physics.

While symmetry is a very intuitive concept, describing it mathematically is more difficult than you might think. First, we have to learn about transformations

, which are ways to convert one geometric figure into another one. Here are a few examples:

The result of a transformation is called the image

. We often denote the image of a shape A as A, pronounced “A prime”. There are many different types of transformation, which we’ll explore in more detail throughout this course.

Archie