In dividing a equilateral triangle into n equal parts with equal areas and equal shapes...

People of Brilliant, how are you all? I came across an interesting puzzle that I want some help solving.

Suppose we want to divide an equilateral triangle into \(n\) equal pieces, with the same area and the same shape. Is it possible to divide such a triangle into \(5\) equal pieces? Is it possible to do it for an arbitrary value of \(n\)?


My investigations showed me that 2 and 3 are the most basic divisions available, and then onward I could find ways to divide a triangle into \(n^2\) pieces, and then either into \(2n^2, 3n^2\) and \(6n^2\). Any hints as to how I can either do it, or prove there is no way?

Note by Alexandre Miquilino
8 months, 3 weeks ago

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If the pieces needn't be contiguous, it turns out it can be done as shown here !!

Anirudh Sreekumar - 8 months, 3 weeks ago

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While this is not exactly a solution I wanted, there is a reference to a paper in another answer which seems to state it is impossible. Thanks for the find!

Alexandre Miquilino - 8 months, 3 weeks ago

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4 join all the midpoints of the sides forming 4 equilateral triangles each of equal area

U K Swamy - 6 months, 2 weeks ago

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4 falls in the \(n^2\) category, but thanks for the input.

Alexandre Miquilino - 6 months, 2 weeks ago

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oh sorry

U K Swamy - 5 months, 1 week ago

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Hi,may I ask that where do you live,which country?

Frost Constantin - 7 months, 2 weeks ago

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