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  2. Equilateral triangle - Wikipedia

    en.wikipedia.org/wiki/Equilateral_triangle

    An equilateral triangle with a side of 2 has a height of √ 3, as the sine of 60° is √ 3 /2. The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base , and the hypotenuse is the side of the equilateral triangle.

  3. Koch snowflake - Wikipedia

    en.wikipedia.org/wiki/Koch_snowflake

    draw an equilateral triangle that has the middle segment from step 1 as its base and points outward. remove the line segment that is the base of the triangle from step 2. The first iteration of this process produces the outline of a hexagram. The Koch snowflake is the limit approached as the above steps are followed indefinitely.

  4. Equilateral polygon - Wikipedia

    en.wikipedia.org/wiki/Equilateral_polygon

    Equilateral polygon. In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need ...

  5. Viviani's theorem - Wikipedia

    en.wikipedia.org/wiki/Viviani's_theorem

    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] It is a theorem commonly employed in various math competitions, secondary school mathematics examinations, and has wide applicability to ...

  6. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...

  7. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.

  8. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.

  9. Square - Wikipedia

    en.wikipedia.org/wiki/Square

    Square. In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides.

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