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Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons. The name suggests the use for isometric views or pseudo-three-dimensional views. Among other functions, they can be used in the design ...
Construction of equilateral triangle with compass and straightedge. An equilateral triangle is easily constructed using a straightedge and compass, because 3 is a Fermat prime. Draw a straight line, and place the point of the compass on one end of the line, and swing an arc from that point to the other point of the line segment.
The two yellow triangles on the ends will end up taped together. The red and blue arcs are seen as full circles on the inside of one side or the other when folded. A hexaflexagon with three faces is the simplest of the hexaflexagons to make and to manage, and is made from a single strip of paper, divided into nine equilateral triangles.
In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər /), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.
In the US, paper density is usually measured in "pound per reams " (of 500 sheets). Typical Letter paper has a basis weight of paper of 20 or 24 pounds (9.1 or 10.9 kg) – the weight of 500 sheets (a ream) of 17-by-22-inch (431.8 by 558.8 mm) paper at 70 °F (21 °C) and at 50% humidity. [3] One ream of 20-pound Letter-sized paper weighs 5 ...
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. [1] It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to ...
The graph perspective allows one to apply graph terminology and properties to polyhedra. For example, the tetrahedron and Császár polyhedron are the only known polyhedra whose skeletons are complete graphs (K 4), and various symmetry restrictions on polyhedra give rise to skeletons that are symmetric graphs.
The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in ...