# 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.

What if applet does not run? |

### References

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

### Fibonacci Numbers

- Ceva's Theorem: A Matter of Appreciation
- When the Counting Gets Tough, the Tough Count on Mathematics
- I. Sharygin's Problem of Criminal Ministers
- Single Pile Games
- Take-Away Games
- Number 8 Is Interesting
- Curry's Paradox
- A Problem in Checker-Jumping
- Fibonacci's Quickies
- Fibonacci Numbers in Equilateral Triangle
- Binet's Formula by Inducion
- Binet's Formula via Generating Functions
- Generating Functions from Recurrences
- Cassini's Identity
- Fibonacci Idendtities with Matrices
- GCD of Fibonacci Numbers
- Binet's Formula with Cosines
- Lame's Theorem - First Application of Fibonacci Numbers

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