Concept
Tetrahedron
Overview
In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.
The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex.
The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".
Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets.
For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's faces.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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1. The part immediately beneath the cranium is called the face in mankind alone, for we do not speak of the face of a fish or of an ox; the part immediately beneath the sinciput and between the eyes is called the forehead. Those in whom this feature is large are tardy; those who have a small forehead are easily excited; a broad forehead belongs to those who are liable to be carried away by their feelings; a round…
Aristotle, Aristotle's History of Animals In Ten Books
States what Tetrahedron is; the author is tied to Tetrahedron in the knowledge graph.
Substance, in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse. But in a secondary sense those things are called substances within which, as species, the primary substances are included; also those which, as genera, include the species. For instance, the individual man is included in the…
Aristotle, The Categories
States what Tetrahedron is; the author is tied to Tetrahedron in the knowledge graph.
In respect to any complex eternal object, _S(D1, D2, ... Dn)_, the eternal objects _D1, ... Dn_, whose individual essences are constitutive of the individual essence of _S(D1, ... Dn)_, are called the components of _S(D1, ... Dn)_. It is obvious that the grade of complexity to be ascribed to _S(D1, ... Dn)_ is to be taken as one above the highest grade of complexity to be found among its components.
Alfred North Whitehead, Science and the modern world
States what Tetrahedron is; names Tetrahedron.
Philosophers who discussed Tetrahedron
Related ideas
- Artificial intelligence
- Golden ratio
- Geometry
- Marvin Minsky
- Triangle
- Aristotle
- Water
- Oxford University Press
- Wiley (publisher)
- Prentice Hall
- Cambridge University Press
- Dover Publications
- Euclidean geometry
- Electromagnetic field
- Absolute value
- Isosceles triangle
Place in the tradition
Part of Pythagoreanism.