"Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria."
The study of how elements on either side of a central axis are arranged in a mirror-image pattern, which was a prominent feature of Renaissance architecture and a reflection of the era's interest in balance and order.
Geometry: The study of shapes and their properties.
Reflection symmetry: The property of a shape that remains unchanged after reflection across a line.
Rotational symmetry: The property of a shape that remains unchanged after rotation around a center point.
Translation symmetry: The property of a shape that remains unchanged after moving it along a straight line without rotating or reflecting it.
Symmetry axis: The line or point around which a shape exhibits symmetry.
Symmetry group: A set of all symmetry operations that can be performed on a shape.
Platonic solids: A set of five regular polyhedra, each of which exhibits high degrees of symmetry.
Archimedean solids: A set of polyhedra with regular faces, but not necessarily regular vertices.
Tessellations: A way of covering a two-dimensional plane with congruent shapes, often exhibiting various kinds of symmetry.
Vertebrate and invertebrate animals: Certain animals, such as butterflies and starfish, exhibit symmetry that is important in their classification and biology.
Fractals: Mathematical patterns that exhibit self-similarity, often with a high degree of symmetry.
Islamic geometric patterns: A rich tradition of geometric art and design that often exhibits symmetry of various kinds.
Crystallography: The study of crystals and their symmetries, important in materials science and chemistry.
Symmetry in music: The use of symmetry in musical composition, especially in the work of minimalist composers like Steve Reich and Philip Glass.
Symmetry breaking: The phenomenon in physics where symmetries of a system are broken, resulting in new emergent behaviors.
Bilateral Symmetry: The most common type of symmetry in Renaissance architecture. The building is symmetrical in two halves, one on either side of a central axis.
Radial Symmetry: The building is symmetrical around a central point, with identical elements radiating out from the center.
Asymmetrical Symmetry: The building is deliberately designed to appear asymmetric, while still maintaining a sense of balance and harmony.
Translational Symmetry: The same pattern or element is repeated at regular intervals along an axis.
Rotational Symmetry: The building is symmetrical around a central point, but instead of having identical elements radiating out from the center, the building has repeated rotational elements.
Fractal Symmetry: The building incorporates self-similar patterns at different scales, giving the impression of infinite complexity.
Reflective Symmetry: The building is symmetrical around a central horizontal or vertical axis, with identical elements on either side.
Helical Symmetry: The building incorporates a spiral pattern, such as a spiral staircase or a helical ramp, that repeats at regular intervals.
Diagonal Symmetry: The building is symmetrical along a diagonal axis, with mirrored elements on either side.
Glide Reflection Symmetry: Similar to translational symmetry, the building incorporates a repeated pattern that is translated but also reflected.
"External symmetry can be easily seen by just looking at an organism."
"For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern."
"Yes, internal features can also show symmetry, for example, the tubes in the human body."
"The tubes in the human body are responsible for transporting gases, nutrients, and waste products."
"Importantly, unlike in mathematics, symmetry in biology is always approximate."
"For example, plant leaves – while considered symmetrical – rarely match up exactly when folded in half."
"While sponges and placozoans represent two groups of animals which do not show any symmetry (i.e., are asymmetrical)."
"These are radial (cylindrical), bilateral, biradial, and spherical symmetry."
"Yes, viruses also contain icosahedral symmetry."
"The importance of symmetry is illustrated by the fact that groups of animals have traditionally been defined by this feature in taxonomic groupings."
"The Radiata, animals with radial symmetry, formed one of the four branches of Georges Cuvier's classification of the animal kingdom."
"Meanwhile, Bilateria is a taxonomic grouping still used today to represent organisms with embryonic bilateral symmetry."
"Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria."
"External symmetry can be easily seen by just looking at an organism."
"Yes, internal features can also show symmetry, for example, the tubes in the human body."
"Symmetry in biology is always approximate."
"For example, plant leaves – while considered symmetrical – rarely match up exactly when folded in half."
"Yes, sponges and placozoans represent two groups of animals that do not show any symmetry (i.e., are asymmetrical)."
"Groups of animals have traditionally been defined by this [symmetry] feature in taxonomic groupings."