MMW

• Symmetry comes from a Greek word symmetria meaning 'to measure together' and is widely used in the study of geometry
• Hop A pattern which only involves translation.
• Step • It is combination of translation and reflection shown by the following figure. Conway also called it glide reflection symmetry.
• Sidle • The third consists of translation and vertical reflection symmetries.
• Spinning Hop • It contains translation and rotation (by half turn or rotation at 180o angle) symmetries
• Spinning Sidle • It contains translation, glide, reflection and rotation (by a half-turn or rotation at 180o angle) symmetries.
• Jump • It contains translation and horizontal reflection symmetries.
• Spinning Jump • It contains all symmetries ( translation, horizontal and vertical reflection, and rotation)
• Frieze patterns are patterns that repeat in a straight vertical or horizontal line. Frieze patterns are found in architecture, fabrics, and wallpaper borders, just to name a few
• A dilation is a transformation that changes the size of a figure. It can become larger or smaller, but the shape remains the same.
• It is a transformation that turns a figure about a fixed point called the center of rotation. Rotations can be done clockwise or counterclockwise.
• Translation and reflection can be combined to yield an effect called gilded reflection
• Reflection is a transformation in which the figure or object is mirror image of the other.
• Translation A mathematical term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way.
• The initial object to be transformed is called pre-image and the transformed object is called image.
• Types of Transformations 1. Translation 2. Reflection 3. Rotation 4. Dilation
• A transformation changes the size, shape, or position of a figure and creates a new figure
• A geometry transformation is either rigid or non-rigid; another word for a rigid transformation is "isometry".
• An isometry, such as a rotation, translation, or reflection, does not change the size or shape of the figure. A dilation is not an isometry since it either shrinks or enlarges a figure
• According to Grünbaum and Shephard, a motif is ”any non-empty plane set” (1987).
• A pattern can be described as “repetitions of a motif in the plane”
• An isometry is the rotation of a motif in a fixed angle about a fixed point. Each rotation of a figure is an isometry. The image of the basic motif under the additional number of rotation is a pattern