Podcast
Questions and Answers
Reflection or ______ symmetry is the simplest kind of symmetry.
Reflection or ______ symmetry is the simplest kind of symmetry.
bilateral
One of the most common kinds of symmetry that we see in the ______ world.
One of the most common kinds of symmetry that we see in the ______ world.
natural
The rosette patterns are those that repeat in no ______ or have rotation symmetry.
The rosette patterns are those that repeat in no ______ or have rotation symmetry.
direction
Cyclic patterns only exhibit ______ symmetry.
Cyclic patterns only exhibit ______ symmetry.
Dihedral patterns exhibit both rotational and ______ symmetry.
Dihedral patterns exhibit both rotational and ______ symmetry.
The frieze pattern only admits translations and vertical ______.
The frieze pattern only admits translations and vertical ______.
Sidle patterns only admit translations and 180° ______.
Sidle patterns only admit translations and 180° ______.
Spinning Siddle patterns only admit translations, vertical reflections, rotations, and ______ reflections.
Spinning Siddle patterns only admit translations, vertical reflections, rotations, and ______ reflections.
A frieze pattern that only admits translations is called a ______.
A frieze pattern that only admits translations is called a ______.
A frieze pattern that admits translations, vertical reflections, horizontal reflections, rotations, and glide reflections is known as a ______.
A frieze pattern that admits translations, vertical reflections, horizontal reflections, rotations, and glide reflections is known as a ______.
A wallpaper pattern is considered valid if it has at least one basic unit that repeats by translation in the second ______.
A wallpaper pattern is considered valid if it has at least one basic unit that repeats by translation in the second ______.
A pattern that covers a plane with no gaps or overlaps is known as a ______.
A pattern that covers a plane with no gaps or overlaps is known as a ______.
The frieze pattern that only admits translational and glide symmetries is termed as a ______.
The frieze pattern that only admits translational and glide symmetries is termed as a ______.
In mathematics, a pattern with translation symmetry in two directions is referred to as a ______ pattern.
In mathematics, a pattern with translation symmetry in two directions is referred to as a ______ pattern.
A frieze pattern extends to the left and right in such a way that it can be mapped onto itself by a horizontal ______.
A frieze pattern extends to the left and right in such a way that it can be mapped onto itself by a horizontal ______.
Mathematics is a branch of science, which deals with ______ and their operations.
Mathematics is a branch of science, which deals with ______ and their operations.
The patterns in a wallpaper can be made up of a combination of symmetries such as reflection, rotation, and ______ reflection.
The patterns in a wallpaper can be made up of a combination of symmetries such as reflection, rotation, and ______ reflection.
A pattern is an arrangement which helps observers anticipate what they might see or what happens ______.
A pattern is an arrangement which helps observers anticipate what they might see or what happens ______.
Mathematics helps us to organize and ______ our ideas about patterns.
Mathematics helps us to organize and ______ our ideas about patterns.
Bilateral-symmetric objects have at least one line or axis of ______.
Bilateral-symmetric objects have at least one line or axis of ______.
Radial or ______ symmetry occurs when an object can be rotated and still looks the same.
Radial or ______ symmetry occurs when an object can be rotated and still looks the same.
Mathematics is a study of patterns and ______, a way of thinking, an art, a language, and a tool.
Mathematics is a study of patterns and ______, a way of thinking, an art, a language, and a tool.
Mathematics involves calculation, computation, and solving of ______.
Mathematics involves calculation, computation, and solving of ______.
Symmetry occurs when there is congruence in ______, due proportions and arrangement.
Symmetry occurs when there is congruence in ______, due proportions and arrangement.
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Study Notes
Mathematics: A Study Of Patterns
- Mathematics is a branch of science focusing on numbers and their operations, encompassing calculation, computation, and problem-solving.
- Mathematics assists in organizing and systematizing ideas about patterns.
Patterns in Nature
- A pattern is an arrangement that helps to anticipate future occurrences or observations.
- Patterns are found in both natural and human-made objects.
Symmetry
- Symmetry occurs when there is congruence in dimensions, proportions, and arrangement.
- Reflection or Bilateral Symmetry is the simplest and most common type of symmetry, often referred to as "mirror symmetry."
- Radial/Rotational Symmetry occurs when an object can be rotated at any degree and maintain the same appearance.
Classifications of Symmetric Patterns
- Rosette Patterns: Repeat in no direction, displaying rotation and/or reflection symmetry.
- Cyclic patterns only exhibit rotational symmetry.
- Dihedral patterns exhibit both rotational and reflectional symmetry.
- Frieze Patterns: Repeat in exactly one direction, extending left and right. They can be mapped onto themselves by a horizontal translation.
- Hop: Translation symmetry only.
- Sidle: Translation and vertical reflection symmetry.
- Spinning Hop: Translation and 180° rotation symmetry.
- Spinning Siddle: Translation, vertical reflection, rotation, and glide reflection symmetries.
- Jump: Translation, horizontal reflection, and glide reflection symmetries.
- Spinning Jump: Translation, vertical, and horizontal reflections, rotation, and glide reflection symmetries.
- Step: Translation and glide reflection symmetries.
Wallpaper Patterns
- Wallpaper patterns repeat in more than one direction, exhibiting translation symmetry.
- They combine reflection, rotation, and glide reflection.
- To be considered a wallpaper pattern, a plane figure must have at least two rows of units, with each row containing at least two units.
Tessellation or Tiling
- A repeating pattern of shapes that covers a surface without gaps or overlaps.
- Similar to wallpaper groups, tessellations create patterns by repeating a shape to fill the plane.
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