UnboundedFigures
UnboundedFigures
✦ Public wall

The Sketch

Raw ideas, half-formed hunches, wild conjectures — all welcome here. Post your mathematical thinking before it's ready. No credentials required. ?The Sketch is a public wall for mathematical intuitions at any stage of development. No gatekeeping — post your idea before it's ready.

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A fleeting feeling — barely a thought, just a direction.A suspicion worth exploring. Something feels true but I can't say why yet.I think there's a theorem here — I just need to find the proof.Explicit call for collaboration. I want someone to formalize this with me.
Filtered by tag:#3n+1
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Tyler Samuels@tsamuels·4d ago
Looking for a Rigorist— Explicit call for collaboration
Plotting Collatz orbits as points draws triangles whose sides give φ
#collatz
#3n+1
#golden-ratio
#number-theory
#discrete-geometry

Intuition

The wedge of triangles feels like a hidden coordinate system for the 3n+1 problem — the same orbits everyone plots as a tree, but the geometry reorganizes them into a self-similar tiling. The golden ratio falling out of the side lengths feels like the geometry is telling me something the arithmetic keeps hidden.

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