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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 Tetractys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the ...
The pedal triangle of an isodynamic point, the triangle formed by dropping perpendiculars from to each of the three sides of triangle , is equilateral, [5] as is the triangle formed by reflecting across each side of the triangle. [7] Among all the equilateral triangles inscribed in triangle , the pedal triangle of the first isodynamic point is ...
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]
A triomino tile is in the shape of an equilateral triangle approximately 1 in (2.5 cm) on each side and approximately 1 ⁄ 4 in (6.4 mm) thick. Each point of the triangle has a number (most often from 0 to 5, as in the Pressman version), [2] and each triomino has a unique combination of numbers, subject to the following restrictions:
The dihedral group D 3 is the symmetry group of an equilateral triangle, that is, it is the set of all rigid transformations (reflections, rotations, and combinations of these) that leave the shape and position of this triangle fixed.
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Van Schooten's theorem, named after the Dutch mathematician Frans van Schooten, describes a property of equilateral triangles.It states: For an equilateral triangle with a point on its circumcircle the length of longest of the three line segments ,, connecting with the vertices of the triangle equals the sum of the lengths of the other two.