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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.
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 ...
Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. [1] It is a theorem commonly employed in various math competitions, secondary school mathematics examinations, and has wide applicability to ...
Schläfli symbol. {3} (for equilateral) Area. various methods; see below. A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero- dimensional points while the sides connecting them, also called edges, are one-dimensional line segments.
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. [1] It is formed from the intersection of three circular disks, each having its center on the boundary of the other two. Constant width means that the separation of every two parallel supporting lines ...
If each vertex angle of the outer triangle is trisected, Morley's trisector theorem states that the purple triangle will be equilateral. In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle.
Napoleon's theorem: If the triangles centered on L, M, N are equilateral, then so is the green triangle.. In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle.
Dihedral group of order 6. (The generators a and b are the same as in the Cayley graph shown above.) Only the neutral elements are symmetric to the main diagonal, so this group is not abelian. In mathematics, D3 (sometimes alternatively denoted by D6) is the dihedral group of degree 3 and order 6.
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