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Record W4376873308 · doi:10.1080/0025570x.2023.2199695

A Simple Proof that π > 3.05

2023· article· en· W4376873308 on OpenAlex
Jake H. Lewis

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueMathematics Magazine · 2023
Typearticle
Languageen
FieldMathematics
TopicHistory and Theory of Mathematics
Canadian institutionsUniversity of New Brunswick
Fundersnot available
KeywordsCalculatorSimple (philosophy)MathematicsCalculus (dental)Series (stratigraphy)Mathematics educationArithmeticAlgebra over a fieldPure mathematicsComputer scienceEpistemologyMedicine

Abstract

fetched live from OpenAlex

SummaryIn classrooms where most students are simply told that π≈3.14, accept the fact, and move on, methods for finding lower or upper bound on π are usually not taught. Here, I consider a University of Tokyo entrance exam problem: Prove that π>3.05, I provide students with a simple, yet nontraditional, proof method. In particular, this method does not require a calculator (as in many exams), cumbersome circle geometry, direct use of calculus-based methods, or partial sums of any infinite series.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.248
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.006

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.066
GPT teacher head0.303
Teacher spread0.238 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it