#mathstodon #mathematicalRecreation #openQuestion

Shower thought from the other day: Is there a generalized continued fraction (https://en.wikipedia.org/wiki/Generalized_continued_fraction) with partial numerators and denominators b0,a1,b1,a2,b2,… (all positive integers)

such that the decimal number it represents is b0.a1b1a2b2a3b3… (concatenation of all the constants)?

Is there a finite one? Are there any? ¯\_(ツ)_/¯

#mathematicalRecreation I don't know the answer to this yet, but it has been bugging me since I woke up for some reason:

Is it possible to fill out a 3x3 square of cells with unique integers, such that every row and column [and diagonal?] contains a Pythagorean triple?

That is, where the three numbers {n1,n2,n3} in any row/column, *in some order*, satisfy a^2 + b^2 = c^2?

It feels like it depends on integers participating in many triples... but big ones do, sometimes?

#nerdsnipe

#mathematicalRecreation [sort of kind of; I got no answer]

What's the largest arithmetic expression tree you can make with only "+", "-", "*" and "/" as its branches, and either "x" (a single unknown real-valued variable") or "k" (a real constant)…

1. using exactly 45 branches+leaves
2. that cannot be reduced algebraically to a smaller tree ?

You can use parentheses as needed.

[example follows]…