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The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (a tree with no vertices, if such are allowed) has depth and height −1. A k-ary tree (for nonnegative integers k) is a rooted tree in which each vertex has at most k children.
For each t ∈ T, the order type of {s ∈ T : s < t} is called the height of t, denoted ht(t, T). The height of T itself is the least ordinal greater than the height of each element of T. A root of a tree T is an element of height 0. Frequently trees are assumed to have only one root.
Young female cone Pinus sylvestris forest in Sierra de Guadarrama, central Spain. Pinus sylvestris is an evergreen coniferous tree growing up to 35 metres (115 feet) in height [4] and 1 m (3 ft 3 in) in trunk diameter when mature, [5] exceptionally over 45 m (148 ft) tall and 1.7 m (5 + 1 ⁄ 2 ft) in trunk diameter on very productive sites.
Pinus lambertiana (commonly known as the sugar pine or sugar cone pine) is the tallest and most massive pine tree and has the longest cones of any conifer. It is native to coastal and inland mountain areas along the Pacific coast of North America , as far north as Oregon and as far south as Baja California in Mexico.
The lateral surface area of a right circular cone is = where is the radius of the circle at the bottom of the cone and is the slant height of the cone. [4] The surface area of the bottom circle of a cone is the same as for any circle, . Thus, the total surface area of a right circular cone can be expressed as each of the following:
The tallest is a coast redwood (Sequoia sempervirens), with a height of 115.55 metres (although one mountain ash, Eucalyptus regnans, allegedly grew to a height of 140 metres, [16] the tallest living angiosperms are significantly smaller at around 100 metres.
The (usually infinite) collection of all these triangles can be (partially) depicted in the shape of a cone with the apex N. The cone ψ is sometimes said to have vertex N and base F. One can also define the dual notion of a cone from F to N (also called a co-cone) by reversing all the arrows above. Explicitly, a co-cone from F to N is a family ...
The cone of Pinophyta (conifer clade) contains the reproductive structures. The woody cone is the female cone, which produces seeds. The male cone, which produces pollen, is usually ephemeral and much less conspicuous even at full maturity. The name "cone" derives from Greek konos (pine cone), which also gave name to the geometric cone.