📏 Any chance of some #maths terminology help here, folks?

We're looking at a board of @simontatham's Loopy, and it's the logic around that squared 2-region I'm interested in.

• The Top edge has already been erased, so cannot count towards the region's total.
• We know that the line entering its bottom-left corner must continue along either its Left or Bottom edge, but not both, thus accounting for 1 of the 2 line segments the region needs drawn.
• Therefore, the Right edge must inevitably be drawn, to bring the region's total to 2.

It's that "optionality leading to inevitability" I'm wondering if there's a term for. Found my way to the Wiki article on Integer partition – https://en.wikipedia.org/wiki/Integer_partition – which I think feels kinda close, and am temped to refer to this logic as "Partitioning". But does anyone with more maths language up their sleeve than me have a better idea?

#Math

Theorem of the Day (June 20, 2026) : The 1-2-3 Conjecture
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/DegreeColourable/TotDDegreeColourable.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#70

#mathematics #maths #math #theorem @Theoremoftheday

A030459: Prime p concatenated with next prime is also prime
A030459 ➡️ https://oeis.org/A030459

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A030459.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A030459.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A030459.html

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Problem for June 20th from the 2026 AMS Daily Epsilon of Math Calendar

@DailyEpsilon

#math #maths #mathematics #mathstodon

My data have not been verified but my work is highly reproducible.
- Downloads (csv, img, dump) ➡️ https://decompwlj.com/
- Algorithms ➡️ https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump#Algorithms

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A030457: Numbers k such that k concatenated with k+1 is prime
A030457 ➡️ https://oeis.org/A030457

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A030457.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A030457.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A030457.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

A030144: Primes in which parity of digits alternates
A030144 ➡️ https://oeis.org/A030144

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A030144.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A030144.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A030144.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

In the decomposition into weight × level + jump, the Twin Prime Conjecture becomes: "The number of prime numbers with a weight of 3 is infinite"

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