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The triangle, viewed face-on, appears equilateral. In (4), the distances of P from lines BC , AC and AB are denoted by a ′ , b ′ and c ′ , respectively. For any line l = s + t n̂ in vector form ( n̂ is a unit vector) and a point p , the perpendicular distance from p to l is
A de Finetti diagram. The curved line is the expected Hardy–Weinberg frequency as a function of p.. A de Finetti diagram is a ternary plot used in population genetics.It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid.
A deltahedron is a polyhedron whose faces are all equilateral triangles. The deltahedron is named by Martyn Cundy, after the Greek capital letter delta resembling a triangular shape Δ. [1] The deltahedron can be categorized by the property of convexity. The simplest convex deltahedron is the regular tetrahedron, a pyramid with four equilateral ...
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
The molecular geometry can be determined by various spectroscopic methods and diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques.
For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.. 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]
Given the edge length .The surface area of a truncated tetrahedron is the sum of 4 regular hexagons and 4 equilateral triangles' area, and its volume is: [2] =, =.. The dihedral angle of a truncated tetrahedron between triangle-to-hexagon is approximately 109.47°, and that between adjacent hexagonal faces is approximately 70.53°.
A 3-simplex with triangular symmetry can be expressed as the join of an equilateral triangle and 1 point: 3.( )∨( ) or {3}∨( ). A regular tetrahedron is 4 ⋅ ( ) or {3,3} and so on. The numbers of faces in the above table are the same as in Pascal's triangle , without the left diagonal.