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‘One way to draw a Reuleaux triangle is to start with an equilateral triangle, which has three sides of equal length.’
‘But the image of the centroid of the equilateral triangle (which is, of course, the point of intersection of its medians) will be different, as indicated in Figure 6.’
‘Then divide it into three equal pieces, and replace the middle piece with the other two sides of the equilateral triangle that has this middle piece as its base.’
‘The Von Koch snowflake is a fractal which is constructed from an equilateral triangle as follows.’
‘An equilateral triangle produces one of the observed crop-circle patterns; three isosceles triangles generate the other crop-circle geometries.’
‘Any given triangle, either imagined or on paper, must either be acute, right, or obtuse, and either scalene, isosceles, or equilateral, and so any given triangle cannot represent all triangles.’
‘For example, it's possible to slice a square into four angular pieces that can be rearranged into an equilateral triangle.’
‘The vibration exciter and geophone were placed near the burrow with burrow opening, exciter and geophone occupying the three corners of an equilateral triangle having sides one meter in length.’
‘Now, both the original Asymmetric Propeller and Napoleon's theorem start with three equilateral triangles and discover the fourth one by construction.’
‘The most interesting results show, with a very ingenious proof, that an equilateral triangle has a greater area than any isosceles or scalene triangle with the same perimeter.’
‘This is constructed by dividing a line into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment.’
‘The sides of this equilateral triangle will be five million kilometres long.’
‘As long as the three triangles are equilateral, the ‘midpoint ‘triangle is also equilateral.’’
‘In 1772, J.L. Lagrange identified a periodic orbit in which three masses are at the corners of an equilateral triangle.’
‘Naturally, the axes form equilateral triangles - 27 of them.’
‘As an equilateral triangle rolls over one catenary, it ends up bumping into the next catenary’
‘For a given individual, the values of the three coefficients in the ancestry vector q are given by the distances to each of the three sides of the equilateral triangle.’
‘An equilateral triangle of side length one is called a unit triangle.’
‘If each edge has the same length and each face is an equilateral triangle, the result is a regular tetrahedron - one of the Platonic solids.’
‘The theorem thus implies existence of the total of 18 equilateral triangles.’
Origin
Late 16th century: from French équilateral or late Latin aequilateralis, from aequilaterus ‘equal-sided’ (based on Latin latus, later- ‘side’).