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  2. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    If we draw both circles, two new points are created at their intersections. Drawing lines between the two original points and one of these new points completes the construction of an equilateral triangle. Therefore, in any geometric problem we have an initial set of symbols (points and lines), an algorithm, and some results.

  3. Isodynamic point - Wikipedia

    en.wikipedia.org/wiki/Isodynamic_point

    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 ...

  4. Steiner inellipse - Wikipedia

    en.wikipedia.org/wiki/Steiner_inellipse

    By comparison the inscribed circle and Mandart inellipse of a triangle are other inconics that are tangent to the sides, but not at the midpoints unless the triangle is equilateral. The Steiner inellipse is attributed by Dörrie [ 2 ] to Jakob Steiner , and a proof of its uniqueness is given by Dan Kalman.

  5. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter .

  6. Steiner ellipse - Wikipedia

    en.wikipedia.org/wiki/Steiner_ellipse

    By comparison the circumcircle of a triangle is another circumconic that touches the triangle at its vertices, but is not centered at the triangle's centroid unless the triangle is equilateral. The area of the Steiner ellipse equals the area of the triangle times 4 π 3 3 , {\displaystyle {\frac {4\pi }{3{\sqrt {3}}}},} and hence is 4 times the ...

  7. Borromean rings - Wikipedia

    en.wikipedia.org/wiki/Borromean_rings

    A stone pillar in the 6th-century Marundeeswarar Temple in India shows three equilateral triangles rotated from each other to form a regular enneagram; like the Borromean rings these three triangles are linked and not pairwise linked, [12] but this crossing pattern describes a different link than the Borromean rings. [13]

  8. Thébault's theorem - Wikipedia

    en.wikipedia.org/wiki/Thébault's_theorem

    Given a square, construct equilateral triangles on two adjacent edges, either both inside or both outside the square. Then the triangle formed by joining the vertex of the square distant from both triangles and the vertices of the triangles distant from the square is equilateral. [2]

  9. Equilateral triangle - Wikipedia

    en.wikipedia.org/wiki/Equilateral_triangle

    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.