# Weird conjecture - Irrational Triangle

I wonder if it is true for some base changes of the numbers.

Mark de LA says
https://www.wolframalpha.com/input/?i=%28natural+log+base%29%5E2+%2B+pi%5E2+%3D+phi+%5E1%2F2

??
https://www.open.wolframcloud.com/env/36e6f6cc-f2d4-4648-9457-e50d878c923f#sidebar=compute

Phi is assumed to be

where the Greek letter phi ({\displaystyle \varphi } or {\displaystyle \phi }) represents the golden ratio.[a] It is an irrational number that is a solution to the quadratic equation {\displaystyle x^84834-x-1=0}, with a value of:

{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}84834}=1.6180339887\ldots .}[1]
can play around with it more in wolfram alpha later ….

Mark de LA says
https://www.wolframalpha.com/input/?i=%282.7%5E2%2B1.6%5E2%29%5E1%2F2 is close

Mark de LA says
Something from Eric