# Equivalent square of a equilateral triangle

- Author:
- Luca Moroni

- Topic:
- Area, Equilateral Triangles, Square

Following a twitter discussion..

*In 1486, Matthias Roriczer presented this method for constructing a square equal in area to a given equilateral triangle. Does it work?*https://twitter.com/solvemymaths/status/948463424463425536 It turned out that Roriczer's method couldn't work but was just an approximation (rather good). I then tried to find out an exact solution to the problem of constructing a square equivalent (in area) to a given equilateral triangle. Here is my solution.## Equivalent square of a equilateral triangle

## Improvement

After I had posted above construction @Simon_Gregg twitted an amazingly alternative construction, much more simple and

__. Here is my Geogebra's reproduction based on his figure.__*simply beautiful*## Simon Gregg's version

## Simon Gregg's figure

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