The star of Bethlehem

Two concentric equilateral triangles with parallel sides. What fraction is orange?

Scroll down for a solution to this problem.


A fraction of 7/24 is orange.

This solution starts by acknowledging that each of the two equilateral triangles can be divided into 9 equilateral triangles with base b and height h.

Now consider triangles GHN and IJN. They are similar and from their bases it follows that the latter has a height threefold that of the former. The orange part can now be calculated as 7bh/2, whereas the total area is 12bh.

Visual solution

David Andriana shows how The star of Bethlehem can be solved in a visual manner.


Finally, a Christmas poem kindly composed by Belladonna.

L’étoile de Noël est en fête
Et illumine la voûte céleste
Vêtu d’oranges pour cette occasion
Elle a également invité les citrons
Échappée de la grande conjonction
Où Saturne et Jupiter avaient rendez vous
L’étoile est là,
Elle scintille pour nous !


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