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Heirs in the square - puzzle of the week


A farmer wants to divide his triangular field among his three daughters. They want identically shaped square fields. Is that possible?



The rapeseed is blooming.

The field, in the shape of a regular triangle, stands out clearly against the green pastures that lie around the field.

The owner of the rapeseed field wants to divide it up so that each of his three daughters gets a field of the same size and shape.

The easiest way would be to connect the corner points of the field with the center of the triangular field.

This would result in three triangular fields.

But the daughters don't want triangular fields - they prefer a square shape.

How must the farmer divide his field?

Even if you hardly believe it at first, a division into squares actually works, as the following sketch shows:

The square does not even have to be a trapezoid.

It can also be comparatively irregular in shape.

The only condition is that the common corner point of all three squares coincides with the center point of the triangle, as in the solution above.

And that two adjacent sides of the quadrilateral, running from the center to the edges of the triangle, form an angle of 120 degrees - just like the solution above.

I discovered this geometry puzzle in the book "The Secret of the Twelfth Coin" by Albrecht Beutelspacher.

In case you missed a mystery from the past few weeks, here are the most recent episodes:

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Source: spiegel

All business articles on 2022-05-15

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