Anthony G. Shannon and John N. Crothers

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 1, Pages 88—90

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## Details

### Authors and affiliations

Anthony G. Shannon

* Warrane College, The University of New South Wales
Kensington, 2033, Australia
*

John N. Crothers

*Warrane College, The University of New South Wales
Kensington, 2033, Australia
*

### Abstract

Square integral lattices with basis vector pairs {(*a*, *b*), (–*b*, *a*)}, where *a* and *b* are successive Fibonacci numbers, are employed to develop intermediate convergence forms of Pythagoras’ Theorem for triangles with integral sides.

### Keywords

- Integral lattices
- Basis vectors
- Fibonacci numbers
- Pythagorean triples

### AMS Classification

- 11B39
- 11D09
- 11H06

### References

- Crothers, J. N. (2013) An introduction to simple modular lattices.
*Advanced Studies in Contemporary Mathematics*. 23(4): 637–653. - Shannon, A.G., Horadam, A.F. (1971) A Generalized Pythagorean Theorem.
*The Fibonacci Quarterly*, 9(3): 307–312. - Shannon, A.G., Horadam, A.F. (1994) Arrowhead curves in a tree of Puythagorean triples.
*Int. J. of Mathematical Education in Science and Technology*. 25(2): 255–261. - Atanassov, K., Atanassova, V., Shannon, A. & Turner, J. (2002)
*New Visual Perspectives on Fibonacci Numbers*. New Jersey, World Scientific. - Hunter, J. (1964)
*Number Theory*. Edinburgh: Oliver and Boyd. - Horadam, A. F. (1961) A Generalized Fibonacci Sequence.
*American Mathematical Monthly*, 58(5): 455-459. - Dickson, L. E. (1952)
*History of the Theory of Numbers, Volume 1*. New York: Chelsea. - Shannon, A. G., & Horadam, A.F. (1973) Generalized Fibonacci Number Triples, 80(2): 187–190.

## Related papers

## Cite this paper

APAShannon, A. G., & Crothers, J. N. (2017). A Fibonacci integral lattice approach

to Pythagoras’ Theorem. Notes on Number Theory and Discrete Mathematics, 23(1), 88-90.

Shannon, Anthony G. and John N. Crothers. “A Fibonacci Integral Lattice Approach

to Pythagoras’ Theorem.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 88-90.

Shannon, Anthony G. and John N. Crothers. “A Fibonacci Integral Lattice Approach

to Pythagoras’ Theorem.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 88-90. Print.