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a rod made of coal, lead, graphite, or dry pigment that is used for writing, drawing, or sketching. It is often encased in a wood or metal holder. Prototypes of the pencil included metal points, lead and silver pins that were inserted into metal holders. Used from the 12th to the 16th century, metal points produced a dark gray tone. The black chalk pencil, which was made of black clayish shale and produced a soft dull shade of black, was introduced in the 14th century. Beginning in the 16th century, graphite pencils and pencils made of charred powdered bone bound with gum were widespread. Graphite pencils provide dull strokes with a slight luster. Charred powdered bone produces mat black marks.
In 1790 the French scientist N. Conte invented the wooden pencil. At about the same time, the Czech scientist J. Hardtmuth proposed the manufacture of writing instruments made of a mixture of pulverized graphite and clay. In principle, this method forms the basis of the modern process of pencil manufacture. Mechanical, or automatic, pencils appeared in the second half of the 19th century and became particularly popular in the 20th century.
Depending on various manufacturing techniques and writing properties, there are different kinds of pencils, including black lead (graphite) pencils, colored pencils, and copying pencils. Pencils are also classified according to their use; for example, there are school, office, drafting, drawing, lettering, carpentry, and cosmetic pencils. There are also pencils used for retouching, marking, and labeling various materials. Special types of pencils include pastels and sanguine (red chalk).
In the USSR lead drawing pencils are made in several degrees of hardness, which are indicated by the letters M (soft), T (hard), and MT (medium hard). Numbers often precede the letters; the higher the number, the greater the degree of hardness or softness. Outside of the USSR the letters B and H are used instead of M and T, respectively.
The writing cores of pencils consist of a tightly pressed, uniform mixture of minute particles of different materials. Lead cores contain graphite, colloidal refractory clay (bentonite), a binder (tragacanth or pectin cement), and fats or wax. Colored leads are made of pigments, kaolin, bentonite, talc, a binder, and fats. Copying, or tracing, leads are made of water-soluble pigments (primarily methylene quinone), graphite, talc, bentonite, and a binder.
There are various types of mechanical pencils. In the split collet type, the lead is propelled by the turning of one of the pencil’s components. The propel-repel-expel type has a button that forces the lead through a bored tip. Multicolored pencils have two, four, or more cores that can be alternately pushed through the holder.
a certain type of family of curves in a plane or a certain type of family of surfaces in space. In analytic geometry, a pencil of lines is the set of all straight lines in the plane that either are parallel (a pencil of parallel lines) or pass through a point O in the plane (a pencil of lines through a point). The point O is called the vertex of the pencil. If the equations of two straight lines of the pencil
A1x + B1y + C1 = 0 A2x + B2y + C2 = 0
are given, the equation of the pencil can be represented in the form
λ(A1x + B1y + C1) + μ(A2x + B2y + C2) = 0
where the parameters λ and μ take on any values but do not simultaneously vanish.
A pencil of planes is the set of all planes that either are parallel or pass through some line, which is called the axis of the pencil.