Hello everybody(adsbygoogle = window.adsbygoogle || []).push({});

I have looked everywhere for some good guides, so the question is:

You probably know the Fibonacci sequence (1,1,2,3,5,8…) but there is a lesser-known sequence called (Pythagoras stairs) generated by a similar recursion formula.

This is a sequence of pairs (Xn,Yn) usually arranged as follows:

1 2

2 3

5 7

12 17

And so on……. It begins with (x1,y1)=(1,1) and the recursion formula is

X{n+1} = X{n} + Y{n}

Y{n+1} = X{n}+ X{n+1}

Prove by induction that always

Y^2 = 2 X^2 ± 1

Pythagoras used this equation to generate rational approximations to (2)^1/2

Thanks in advance for usefully discuss to solve for this interesting question

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The idea about Pythagoras stairs?

Loading...

Similar Threads - idea Pythagoras stairs | Date |
---|---|

A Anyone can have the idea how to solve the log of a power ser | Aug 15, 2016 |

Ideas on how to easily solve this long derivation? | Apr 7, 2016 |

Trying to self-learn calculus but stuck on this idea | Dec 2, 2014 |

Weird idea (gradients and potentials) | Aug 31, 2014 |

Double Integral of Pythagoras over rectangular region | Jul 2, 2014 |

**Physics Forums - The Fusion of Science and Community**