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Branch
A branch, sometimes called a ramus in botany, is a woody structural member connected to the central trunk (botany), trunk of a tree (or sometimes a shrub). Large branches are known as boughs and small branches are known as twigs. The term ''twig'' usually refers to a wikt:terminus, terminus, while ''bough'' refers only to branches coming directly from the trunk. Due to a broad range of species of trees, branches and twigs can be found in many different shapes and sizes. While branches can be nearly vertical and horizontal, horizontal, vertical, or diagonal, the majority of trees have upwardly diagonal branches. A number of mathematical properties are associated with tree branchings; they are natural examples of fractal patterns in nature, and, as observed by Leonardo da Vinci, their cross section (geometry), cross-sectional areas closely follow the da Vinci branching rule. Terminology Because of the enormous quantity of branches in the world, there are numerous names in Engl ...
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Branches (DSC 0326)
A branch, sometimes called a ramus in botany, is a woody structural member connected to the central trunk (botany), trunk of a tree (or sometimes a shrub). Large branches are known as boughs and small branches are known as twigs. The term ''twig'' usually refers to a wikt:terminus, terminus, while ''bough'' refers only to branches coming directly from the trunk. Due to a broad range of species of trees, branches and twigs can be found in many different shapes and sizes. While branches can be nearly vertical and horizontal, horizontal, vertical, or diagonal, the majority of trees have upwardly diagonal branches. A number of mathematical properties are associated with tree branchings; they are natural examples of fractal patterns in nature, and, as observed by Leonardo da Vinci, their cross section (geometry), cross-sectional areas closely follow the da Vinci branching rule. Terminology Because of the enormous quantity of branches in the world, there are numerous names in Engl ...
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Tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller palms, tree ferns, bananas, and bamboos are also trees. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically ...
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Tree Leaves
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller palms, tree ferns, bananas, and bamboos are also trees. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically co ...
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Tree Forks
A tree fork is a bifurcation in the trunk of a tree giving rise to two roughly equal diameter branches. These forks are a common feature of tree crowns. The wood grain orientation at the top of a tree fork is such that the wood's grain pattern most often interlocks to provide sufficient mechanical support. A common "malformation" of a tree fork is where bark has formed within the join, often caused by natural bracing occurring higher up in the crown of the tree, and these bark-included junctions often have a heightened risk of failure, especially when bracing branches are pruned out or are shaded out from the tree's crown. Definition In arboriculture, junctions in the crown structure of trees are frequently categorised as either branch-to-stem attachments or co-dominant stems. Co-dominant stems are where the two or more arising branches emerging from the junction are of near equal diameter and this type of junction in a tree is often referred to in layman's terms as 'a tree ...
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Da Vinci Branching Rule
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. In the 20th century, the British mathematician Alan Turing predicted mechanisms of morphogenesis ...
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Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ...
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Willow
Willows, also called sallows and osiers, from the genus ''Salix'', comprise around 400 speciesMabberley, D.J. 1997. The Plant Book, Cambridge University Press #2: Cambridge. of typically deciduous trees and shrubs, found primarily on moist soils in cold and temperate regions. Most species are known as willow, but some narrow-leaved shrub species are called osier, and some broader-leaved species are referred to as sallow (from Old English ''sealh'', related to the Latin word ''salix'', willow). Some willows (particularly arctic and alpine species) are low-growing or creeping shrubs; for example, the dwarf willow (''Salix herbacea'') rarely exceeds in height, though it spreads widely across the ground. Description Willows all have abundant watery bark sap, which is heavily charged with salicylic acid, soft, usually pliant, tough wood, slender branches, and large, fibrous, often stoloniferous roots. The roots are remarkable for their toughness, size, and tenacity to live ...
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