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Angles and triangles
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
An equilateral triangle is one in which all the sides and all the angles are equal; i.e. each is 60∘. An example is shown in triangle ABC in Fig. 21.16(a).
Angles and triangles
Published in John Bird, Basic Engineering Mathematics, 2017
An equilateral triangle is one in which all the sides and all the angles are equal; i.e. each is 60∘ $ ^{\circ } $ . An example is shown in triangle ABC in Fig. 21.16(b).
Series, Taylor’s theorem and its uses
Published in Alan Jeffrey, Mathematics, 2004
Show that for a given perimeter, the equilateral triangle has maximum area. (Hint: Consider the function F(a,b,s) =s(s − a) (s−b)(a+b−s).)
Describing the geometric difference of architectural forms in three primary shapes of circle, triangle and square
Published in Journal of Asian Architecture and Building Engineering, 2022
An equilateral triangle is a three-sided plane with all sides equal and equiangular. A building facade in a triangular shape with the vertex pointing upwards converges the most at the apex, facilitating stability and reliability in building design. Heavy base and the pinnacle on the top in many A-framed residential homes enable handling weight because of how the energy is distributed throughout the triangle; the symmetry in the equilateral triangle and the isosceles triangle aids in distributing weight. Trusses exist as bearing structures because of the inherent triangles provided by struts and other bracing elements (Lenartowicz 2014). The Pyramid in Giza, composed of four equilateral triangular faces, has stood for over 4,000 years. The equilateral triangle encloses the smallest area in the most extended perimeter and is a basic unit representing the three-dimensional surface. On the other hand, it can be seen that the triangular-shaped floor plan is unpractical from a functional point of view, as walls converging at an acute angle of 60° contain narrow leftover margins.
The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means
Published in International Journal of Mathematical Education in Science and Technology, 2022
Thus triangles with side lengths will tend to an equilateral triangle and their areas form a monotonic increasing sequence. This is consistent with the well-known fact that among all triangles with a given perimeter, an equilateral triangle has the maximum area.