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How Many Triangles?
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A selection process used by some compilers of big-prize competitions is to present a triangle (usually equilateral) divided into (say) nine congruent sub triangles by the lines joining corresponding trisection points of the sides, and to ask how many triangles there are in the figure. It is amusing to obtain the general result when each side of the original triangle A is divided into
n
equal parts and pairs of dividing points are joined by parallels to the sides in all possible ways.
Title: How Many Triangles?
Description:
A selection process used by some compilers of big-prize competitions is to present a triangle (usually equilateral) divided into (say) nine congruent sub triangles by the lines joining corresponding trisection points of the sides, and to ask how many triangles there are in the figure.
It is amusing to obtain the general result when each side of the original triangle A is divided into
n
equal parts and pairs of dividing points are joined by parallels to the sides in all possible ways.
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