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Record W4306155752 · doi:10.1017/mag.2022.115

Archimedes playing with a computer

2022· article· en· W4306155752 on OpenAlex

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

VenueThe Mathematical Gazette · 2022
Typearticle
Languageen
FieldMathematics
TopicHistory and Theory of Mathematics
Canadian institutionsUniversité de Sherbrooke
Fundersnot available
KeywordsInscribed figurePolygon (computer graphics)MathematicsCombinatoricsCircumferenceIncircle and excircles of a triangleRADIUSUpper and lower boundsSquare (algebra)Bounded functionInterval (graph theory)GeometryMathematical analysisComputer science

Abstract

fetched live from OpenAlex

It was known before Archimedes (287-212 BC) that the circumference of a circle was proportional to its diameter and that the area was proportional to the square of its radius. It was Archimedes who first supplied a rigorous proof that these two proportionality constants were the same, now called π [1]. He started with inscribed and circumscribed hexagons and increased the number of sides from 6 up to 96 by successively doubling it. His result was not a single value. In fact he generated five intervals each of which contained π. He calculated a lower bound from the inscribed polygon and an upper bound from the circumscribed polygon of 96 sides. This gave him the interval () or (3.140845, 3.142857), which is less accurate than the interval bounded by half-perimeters of the inscribed and circumscribed 96-gons, which is (3.141031, 3.142714).

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
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 score0.204
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0020.000

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 head0.041
GPT teacher head0.266
Teacher spread0.225 · 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