Fibonacci Numbers in Equilateral Triangle

In an equilateral piece of a triangular lattice, color the top triangle and one below. Then continue coloring isosceles trapezoids that are obtained by cutting off rhombi with sides on two colored shapes.

Then, the sides of successive rhombi form a Fibonacci sequence (1,1,2,3,5,8,...) and the top, sides and base of each trapezoid are three consecutive Fibonacci numbers.


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Fibonacci Numbers in Equilateral Triangle


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References

  1. Brian J. McCartin, MYSTERIES OF THE EQUILATERAL TRIANGLE, First published 2010, p. 68
  2. Hans R. Walser, Proof Without Words: Fibonacci Trapezoids, Mathematics Magazine, Volume 84, Number 4, October 2011, pp. 295-295(1)
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